The requirements are usually not set by your PCB manufacturer they are set by you.
Two problems arise when traces are small:
1) More resistance, this causes power loss, it also 'creates' a resistor that was not on your schematic which can cause unintended operation. Make sure the resistance will not be a problem for your design (as small as it may be)
2) Self heating from power loss, while related to resistance, extra heat on your board may create a problem for components or even your board. If the temperature rise is too high (~100C) it can cause delamination of the layers. Tens of degrees higher then that and the board will start to burn. Make sure your power loss is not going to cause a destructive temperature rise.
The second thing to consider is how long will you be drawing the 2A of power, is it a max current rating or an average power rating, if it only draws 2A for 1s every minute or so, your average power will lower and can be considered differently in a temperature rise situation. If it draws 2A all the time then you would size the trace larger.
The other thing to consider is board size, if you have lots of room, make the traces bigger and don't worry about the calculations. If your board size really is a limiting factor, then go to a higher weight of copper which makes the traces taller and cuts back on resistance.
As far as the SMT pads go, they are what they are, and they are sized appropriately. You can run bigger traces into a smaller pad to cut back on resistance, realize that more copper around a pad can make it harder to solder because it wicks heat away from the part when soldering which can make it harder to hand prototype.