I don't think I have any 10s chains.

However, when I first made the jump to 9s, I had a slightly used chain + quick link that I tried. The quick link disintegrated within a couple of days. So, I decided to try a 6/7/8 chain on the bike. Friction shifted.

I rode it for a few miles, but I just couldn't get the trimming right to keep the thing from chattering. So, within a couple of days riding, that chain was removed, and I sourced the proper chain. I think maybe a couple of gears were ok, probably the smallest sprockets.

As far as 11s, most of my cranks and chainrings I'm using aren't 11s. But, I use a chain to match the rear cassette.

The 10s chain should work fine on the 11s chainrings, with perhaps an issue of cross-chaining small/small.

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.