I've found my chip and signature Amex Platinum Card to be just as useless in Europe as my old magstrip-only card.

That's surprising; chip and signature exists in part for accessibility reasons and everywhere is meant to accept them.

I had a really tough time with credit cards in Denmark.

I had one chip & sig card that didn't work except in like one restaurant I went to. A couple of places I could use any regular credit card though. Ended up having to go to ATMs and carry cash, which is so uncommon that people think you're a drug dealer. :D

Bank of America has a similar one too, and it doesn't have a yearly fee.

While I don't have that Chase card, I do know very well that most BofA branded cards have far less lucrative rewards than many of their competitors. FIA has a few great cards and they're owned by BofA. But even when I became a so-called "platinum privileges" bofa customer their best card was not very attractive.

Flat 2% cashback cards are great. Rotating 5% category cards a great. Big signup bonuses are great.

I have a Chase British Air card I opened with a 100,000 mile bonus, plus a companion pass once a certain spending level was reached. Long story shorter, we opened two (one for me, one for my wife). Pooled the miles together. We have 220k miles and a companion pass. We're using this for 2 first class tickets from SFO to Europe in the spring. That is, literally, $25,000 in airfare.

Oh, and it's chip + sig :)

tl;dr Often annual fees are very worth it. And also often, an issuer will waive them in all or part.