Although at 3/4" thick solid-wood panels made from strong hardwoods such as white oak or hickory are plenty stiff, there's a fair bit of unsupported span on designs like this so some minor tweaks would be beneficial IMO.
When there's too much unsupported material on L-shaped desks even gentle pressure from leaning on the surface in the key working zone at or near the inside corner adds a lot of strain and I've had a look at a few commercial desks with no front support which did sag. The dip is usually not excessive, not enough to cause structural concerns certainly, but still is more than I'd find acceptable in normal use.
And it is important to build for the what-if scenario, like if someone were to sit on the desk right in the middle; it's designing for this sort of occurrence that makes additional support highly desirable to semi-essential.
So for this reason I think
- one or more diagonal supports coming up from the rear legs;
or
- a supporting 'batten' spanning the gap between rear legs;
are important additions.
Diagonal support
Diagonal supports don't have to extend too close to the front edge, where they might interfere with sitting, and to save on hardwood these could just be triangles of plywood. Any such support would be invisible when working at the desk but could be seen from further back, so if the aesthetics are important then I think solid-wood struts win over plywood triangles here.
Batten
But a batten board joining the outsides of the rear legs, acting as a beam of sorts, could provide nearly equivalent support and would be completely hidden from view. The more you move the legs out from the corner as you suggest in the Comments the further forward this board is positioned and the more support it adds, but, the longer it needs to be naturally.
Here again this could be made from plywood rather than solid wood (e.g. two strips of 3/4" laminated together, edge-up) so it won't add a lot to the cost. I'm assuming material being bought for this project specifically, rather than scraps of wood/ply1 being used up.
Outside legs
If you want to keep the current outside leg positions because you think this looks best then don't change this part of the design, but if you're not wedded to them being where they are in the image I wanted to suggest you move them inboard of the ends.
The accomplishes 2 1/2 things:
- It great reduces the unsupported spans.
- It makes the table easier to hold on to when moving fully assembled.
- I think it looks better, but obviously this is a YMMV kind of thing :-)
So I think this will remove any need of aprons, reduce build time and material costs.
Desktop joint
I go back and forth about which I prefer for these purely in terms of looks, but once you have to factor in wood movement things get more complicated. I am fond of the look of a 45° join in work surfaces and L-shaped desks with chipboard/particleboard but they're problematic if you're dealing with solid wood2.
Also something that might not be immediately evident, there's the potential for far more wasted wood with a 45° joint — the shorter panel which currently can be made with all boards a smidge over the final 50" length would have to include at least one board a little over 75" long.
So the joint as pictured might seem totally the way to go, but this is a cross-grain situation.....
Remember, to allow for movement: the longer panel has to be able to move away from this joint (expand to the left in the image) OR to push and pull the shorter panel with it as it expands and contracts during seasonal changes in humidity, while still allowing the shorter panel to be free to expand and contract forward from its back edge.
1 If you'd prefer to use solid wood but have no single board long enough, this is a prime candidate for a glued-up piece that uses up multiple scraps, or board-stretching technique (using a long diagonal cut) if you have one board that is close to the length needed but not quite.
2 They can be a much-magnified version of wide mitre joints, which became something that carpenters preferred not to do because of their proven likelihood of opening up at the inside or outside over time.