If the OP is regularly dropping a chain up front, my guess is that it has to do with either excessive chainring wear, or poor derailleur adjustment.

Do you manually trim the front derailleur if you hear rubbing?

Issues on the rear? It is hard to say. That is where one would more likely notice chattering from a wide chain. I suppose ignoring chatter, one could potentially cause excessive cassette wear. Or, perhaps if the chainrings were toast before the new chain, the cassette was too.

I'm not sure about other issues with the rear derailleur. I suppose if things are way out of adjustment, then one could potentially get ghost shifts pulling things sideways.

I have to agree with others... that to some extent this falls on the rider. One should be able to ride the bike around the block and notice that something is way off. Then ride right back to the shop to get it fixed.

I would encourage the OP to carry at least a minimal set of tools, and to know how to use them. If something is stuck, then don't force it, but rather fix it, whether this means removing chainrings or guides.