As the collector-emitter voltage changes, collector current changes due to the Early effect so the base current must also change.
In the small signal model, we only account for the change of collector current due to Vce changes by adding r node resistor in parallel to current source.
Why don't we account for the change in base current due to Vce changes in the small signal model?
I prefer to return back to the original papers when trying to explain (or understand) an effect. If you were taking a class in the 1960's, you'd be taught the details. But modern teaching has so much else to cover and it usually sacrifices deeper approaches that include a physical understanding in the interests of getting on with the business of teaching the necessaries of practical models. Understanding it is left to the student per their own time and inclinations.
The paper you want to read is "Effects of Space-Charge Layer Widening in Junction Transistors" by J. M. Early. (Who is known to have disliked the name "Late Effect" -- later added to the Gummel-Poon BJT model.)
I'll borrow Figure 1 from his paper:
Here, Dr. Early is showing a simplified model of the NPN BJT. The base region thickness is labeled as \$W\$ and the collector's barrier thickness is labeled as \$X_{_\text{M}}\$. (The emitter barrier is usually forward-biased and it is so thin that it can be neglected in the diagram.)
If the reversed collector potential (relative to the base potential) is increased in magnitude, \$X_{_\text{M}}\$ also increases in thickness. But it doesn't go in just one direction, spreading outward into the collector region, as Dr. Shockley earlier assumed (and then used this incorrect assumption to mathematically prove that the collector current was independent of the collector reverse potential -- wrong.) Instead, \$X_{_\text{M}}\$ spreads in both directions (but not necessarily equally so.) The portion spreading into the base region has the effect of reducing thickness \$W\$.
This decrease in \$W\$ decreases the probabilities and therefore the rate of recombination of charges in the base layer as the collector current passes through the now-thinner base layer (charges spend less time transiting there.) This therefore increases the effective transport factor, \$\beta\$. (Note that we've since lost the use of that phrase, too.)
(This also leads to changes in the distributed, but usually lumped, impedances such as the base and emitter impedances. But that's not part of your question or the model you are currently exposed to.)
why don't we account for change in base current due to Vce changes in small signal model?
The small-signal model you are being exposed to is based upon the non-linear, large-scale, hybrid-\$\pi\$, but applying calculus to derive from that a linearized small-signal model. This linearized version of that particular Ebers-Moll model (there are three completely equivalent models, as you can see at the link) is just the tangent line at some point along this "level 1" Ebers-Moll model.
The level 1 (and level 2, later) Ebers-Moll model was developed before the Early Effect was described and therefore does not include it. These earlier models were modified, in the level 3 version, to include a new parameter called the Early voltage as a way of accounting for how the width of the base is modulated by the base-collector reverse voltage magnitude:
(The above image comes from Ian Getreu's "Modeling the Bipolar Transistor." on page 45.)
Those slopes are relatively linear over a useful range and, because they relate voltage and current, can be seen as an added resistance to the small scale model.
However, they are not modeled in the BJT in that fashion in Spice. Nor should they be. That resistance is strictly a small signal equivalent and it only applies to the linearized small-signal model. The large-scale model that Spice must use does not include such a beast. Instead, when using the level 3 Ebers-Moll model (or Gummel-Poon) it modifies the forward transport factor \$\beta\$, the saturation current, and the forward transit time.
The above page extract from this website. The link in the aritcle is here.
As you can see, current passing through \$R_{OSS}\$ does not affect base current.
Let us avoid mixing large-signal operation and small-signal one for now as it only makes things more confusing.
Consider for example a NPN BJT so not to make the discussion overly generic. From the PN junction theory, it is known that (i) device current entails both carrier types (holes and electrons contemporaly) but, if asymmetric doping is used (i.e. one junction much more doped than the other), the other contribution becomes negligible; and, more notably, (ii) PN is a minority carrier device i.e. majority carriers are limited (in the sense of their current density amplitude) by the quasi-neutral region where they are minority carriers and hence hereby a "bottleneck" is present. So for an \$n^+-p\$ device, electrons are limited by the p quasi-neutral region -- by how much, it is quantified in the Gummel number of that region.
Now, for the BJT, the base current contains different contributions since the two junctions must interact to establish a transitor effect (instead of "back-to-back" diodes). Under forward bias (high enough to exclude low-current regimes), the Emitter current is limited by the Base-QNR (hence, the Emitter current depends on the Base Gummel number). The presence of a negative BC bias triggers the Early effect, since as the field gets higher in the base, the depletion layer widening determines a reduction of the Base-QNR, reducing the Base Gummel number, thus increasing the collector current.
The Base current however does not change. This current indeed depends on Emitter-QNR parameters, which are not changed by the CB bias, so there's no Early effect. This is why an increase of \$\beta_{F0}\$ is accounted, since from \$I_C = \beta_{F0}I_B\$ if Ic increases but Ib doesn't, then beta must increase.
Firstly, Early effect is about the collector-base voltage, not the collector-emitter voltage although it is often talked about in terms of the collector-emitter voltage.
My understanding of this is that Early Effect can manifest itself in three ways:-
Hold the base-emitter voltage constant and increase the collector-base voltage. In this scenario, Early Effect can be seen as an increase in collector current as the collector-base voltage is increased. The collector current has increased, the base-emitter voltage has been held constant and the base-emitter current is also unchanged leading to an increase in hFE.
Hold the collector current constant and increase the collector-base voltage. In this scenario Early effect can be seen as a reduction in base-emitter voltage. The base-emitter voltage has reduced and so has the base-emitter current so (as in 1)) hFE has increased.
A combination of 1) and 2). In some circuit arrangements an increase in collector-base voltage can cause Early Effect to show itself as an increase in collector current and simultaneously as a reduction in base-emitter voltage (and base-emitter current), but if the circuit allows the base emitter voltage to reduce then the increase in collector current will not be so large as it would have been if the base-emitter voltage had been held constant. In this combinational scenario the increase in hFE is accounted for partially by an increase in collector current and partially by a decrease in base current.
