Most high level players a good at nullifying the option degradation that missiles cause. By either attacking or dodging the missiles, they don't allow themselves to be limited by missile approaches.
That said, they are merely mitigating losses, as they do have to react in some way. What your job to do is fire missiles and see how they react. If their standard reaction to missiles is to shield them, then running in with a grab or strong attack would be fairly safe and would reduce their shield to a point where they can't reasonably stay in it for long (giving you more openings to be aggressive). If they don't engage with the missiles and aim to avoid it, recognize their escape path and capitalize on it in the future. If they attack missiles with an aerial, then the move will continue after the hit and you can punish according to which aerial they used. If they react by attacking the missiles from the ground, there isn't a solid punish for it. You could react by firing a CS right after the missiles and let their muscle memory get them hit, but then you are gambling on the other person being unobservant (not necessarily bad, just not optimal). For most characters, this is the safest option. Attacking a missile from the ground with a medium-light move will cause it to 'clank' with the missile and cancel the move. For instance, most jabs can stop a missile, cancel quickly, and allow the player time to react to any follow-up you make.
When using MC approaches, be aware of what your opponent is capable of doing to stop it, but, more importantly, see which tools they are using and use that information to your advantage. Following your missile into an attack is viable, but it may require some conditioning/reading/reacting to make it work.
That said, they are merely mitigating losses, as they do have to react in some way. What your job to do is fire missiles and see how they react. If their standard reaction to missiles is to shield them, then running in with a grab or strong attack would be fairly safe and would reduce their shield to a point where they can't reasonably stay in it for long (giving you more openings to be aggressive). If they don't engage with the missiles and aim to avoid it, recognize their escape path and capitalize on it in the future. If they attack missiles with an aerial, then the move will continue after the hit and you can punish according to which aerial they used. If they react by attacking the missiles from the ground, there isn't a solid punish for it. You could react by firing a CS right after the missiles and let their muscle memory get them hit, but then you are gambling on the other person being unobservant (not necessarily bad, just not optimal). For most characters, this is the safest option. Attacking a missile from the ground with a medium-light move will cause it to 'clank' with the missile and cancel the move. For instance, most jabs can stop a missile, cancel quickly, and allow the player time to react to any follow-up you make.
When using MC approaches, be aware of what your opponent is capable of doing to stop it, but, more importantly, see which tools they are using and use that information to your advantage. Following your missile into an attack is viable, but it may require some conditioning/reading/reacting to make it work.