Good beer, good food, Brussels, Netherlands and Germany? This is right up my alley (Caveat to all the below - we haven't been back since 2018 so some of the restaurant and beer notes might be dated):
I'll echo that I found Schipol just fine. Not sure if this matters to you at all but both FRA and AMS have showers you can use on arrival to the airport. Since most flights from the US arrive in the morning and well before normal check-in times* I usually take advantage of these to feel refreshed and ready to start a day of sightseeing.
*With travel suppressed still you might be lucky and be able to check-in but its ~$10 for a shower at the airport and both FRA and AMS have nice facilities
You don't need a car in Belgium and the Netherlands as both have great train options to the places you'll want to go. For both countries your ticket is good on any train to that destination that day. So if you buy a round trip ticket you can come back to your home base whenever you want. Like the city and want to stay later? Go ahead as long as you catch the last train back to your home base you're good to go. Belgium takes that one step farther - you can get off at any stop on the way to your destination for as long as you want. For example you could take a train to Bruges and hop off at Ghent for however long you want before catching a train the rest of the way to Bruges (This is just an example as you'd probably want a decent amount of time in both cities). When we were in Belgium in 2018 we just stayed in Brussels and did day trips by train to places like Bruges and Ghent. Luxembourg (the city) was only ok but there are a lot of nice places you can hit on the way to\from like Vianden and Dinant.
One of the benefits to using a home base in Belgium is that you can get a place with a fridge and store all the great beers you'll come across and leave your luggage for those day trips. So no packing up and looking for luggage storage locations. As for beer you don't have to go to a fancy bottle shop or anything, just hit up a large grocery store and marvel a the vast selection of joyously cheap high quality beers. The Carrefour Market in central Brussels has a great selection. That said, if you want some of the harder to get beers (say a Westvleteren 12) The Bottle Shop in Bruges has the best prices I saw while I was there. And a great selection there too.
Another benefit is that you have some added flexibility in travel plans. Since there is no advantage to booking intra-country trains in advance you can play things by ear. Pouring down rain? Well, don't head to Ghent that day and spend your day drinking around the many bars in Brussels. Oh it cleared up and you aren't totally sloshed yet? Well sure go head to Ghent for the afternoon\evening (Its ~30min away by train)
If you like Fish&Chips give Bia Mara a try and get the extra sauces. I love this place and make a point of eating here at least once (usually twice) when we're anywhere near one (There is one in Antwerp now too). Fritland is worth a stop too. Some give it a hard time as being too touristy but we still like it
Since you mention beer if you head to Dinant you really should stop by Maison Leffe. Good tour and history plus a tasting room with a lot of Leffe options to sample
We didn't find Rotterdam all that interesting. It wasn't bad and we're glad we went but if you haven't been to Belgium or the Netherlands before I'd skip it.
For Amsterdam if you want to go to the Anne Frank house make sure to book well in advance. If you like cheese then make sure to try some of the Gouda varieties and, if you're a fan, take some wheels home. It's a hard cheese so customs is NBD although if you bring a lot back in your carry-on you'll get stopped at all the security xray machines and then get laughed at. But the quality is amazing and you have a lot of very well aged gouda that keeps for a while (you can usually ask for more cheese cloth or paper at the shop to help with long term storage at home). If you really like gouda then see if the town of Gouda has a cheese event while you're in the area (if they don't - skip the town). Zaanse Schans is an easy to get to by public transportation area to see several windmills.
There's not a lot to see in Frankfurt itself - its a commuter\business city so you wouldn't need much time here. And its been
a lot longer since I was in this area of Germany so not much to add to this part of your plan. Still I'm wondering if you could do a routing like this: Frankfurt (1 day) -> Luxembourg (2 days. 1 day for the city the next for Vianden) -> Brussels for several (5?) days (with day trips to Dinant, Bruges, Ghent and maybe Antwerp. Or maybe head to Dinant for a full day - you might be able to do this on the way to Brussels from Luxembourg) before heading to Amsterdam (2 days) and maybe Utrecht (1 day). It doesn't get you to Bonn/Koln/Dusseldorf but hits a lot of other places and you could do that all by train. If you want to cram more time in with some more luggage logistics you could hit the highlights of Frankfurt in a morning and head to Luxembourg by afternoon\evening train if those train options exist to save time. You could also head out from Vianden\Luxembourg the evening\afternoon of the second day there and maybe get to Dinant in the evening, spend the morning to early afternoon there before heading to Brussels. That would give you extra time to hit something else
For planning anything with trains my go to is
always seat61.com. Want to know what easy train options you have from Frankfurt, their time, how much they cost, is first class worth it, pictures of the trains, and how to buy? Here you go:
https://www.seat61.com/international-trains/trains-from-Frankfurt.htm
What about Brussels?
https://www.seat61.com/international-trains/trains-from-Brussels.htm
Amsterdam?
https://www.seat61.com/international-trains/trains-from-Amsterdam.htm
Edit: Belgium is one of my favorite countries so my example itinerary is biased by that so YMMV