the smoke coming from firing missiles could mess with its engine through the inlets.
Consider the design of the F-14 and SU-27 and you will see these planes to be even more prone to such effects than the YF-23, which had its intakes widely spaced apart.
The YF-23 missile launcher was quite capable of making test launches of the AIM-120. In fact test were made with the missile extended almost fully out in the airstream. This way Northrop could simulate unlimited times missile launch without dropping the missile itself.
There was no requirement to perform actual missile launches. There was a requirement however to provided verification data regarding the launching mechanism.
The reason the YF-22 team did that (I think) is because that was the only way to provide the same kind of date the YF-23 team did. Remember how the YF-22 launcher works. The missile cannot be extended into the open and then dropped. Instead, it was pneumatically ejected. So, you cannot test that effect without dropping the missile. And they did eject the missile for the test. It was not really a big deal to make the missile fire its engines afterwords.
The approach by Lockheed made for a very powerful pro YF-22 argument to those not familiar with the actual tests. Actually Northrop tested its simulated missile launches and weapons bay performance at speeds up to Mach 1.5, while Lockheed made all test launches subsonically.
Consequently F-22A did have redesigned weapons bay since the old design could not operate well supersonically. Needless to say the F-23A didn't. It had the same main weapons bay door design.
All in all both teams demonstrated the most critical part of their missile launchers. For YF-22 that was the pneumatic missile ejection and for YF-23 that was bringing the missile from a storage position to launch ready one.
This plane would have been the best F-14 replacement. Better than the F/A-18 Superhornet and the F-35 JSF although some years older.
Yes, it was a bigger airplane all right. But at what cost would it have fully worked? The only thing one could argue is that Northrop/MDD have a lot more carrier experience that Lockheed/Boeing/GD