Should an amp have a "personality"?

Neutral, Natural,  what is it really.  I've had different amps with near identical frequency response,  yet one amp was fast, dynamic, while the other had flow & rhythm.  I've had others that sounded excellent with a perfectly flat speaker,  change to another perfectly flat speaker that had a very different load and it sounded different.  
Amps personality changes with different gear.  There is something to be said for synergy.  

The nice thing about Audiogon is that you can get some nice used gear at a good price if your patient and ultimately sell your amp if it isn’t performing the way you want. As you’ve noted you’re interested in tubes. . . If your not listening at ear splitting volumes you may be able to get a nice tube amp that can sound great and perform with your system. It might be worth a try.

I’ve tried a few amps and noticed that they all had different sounds. My ultimate goal is to project exactly what the performers played so I opted for amps that have high dynamic range and power and an extremely low noise floor. As Inna and others have said the music needs ultimately be engaging. 

Other things that that could be an issue is your room. I’ve found the biggest impact on sound quality is speakers and then a close second is the room, third would be my amps. I hate moving because I have to look at a ton of places to be able to fit my stereo / home theater set up in a room with good acoustics. Unfortunately that quality isn’t located on a listing. You may have some room nodes at the critical middle listening range that are sucking the life out of the room/music. You can try to move your speakers into the room away from walls as much as possible or get a little more technical and get a basic USB Mic and use Room EQ Wizard to see that it looks like. Some time investment in learning to read the room will help you to know where your issue is or if there is one at all so you know if you’re chasing down the correct rabbit hole. 

-Steve

It's true that many can't afford great tube amps...my world class Dennis Had hand made SE HO (it's a HO...it says so right on the front of the thing) was barely used (has its birthday with Had's signature on the bottom plate) when I bought it for around 1200 bucks. Who has that kind of money lying around? And the Freya preamp...700 clams! Whew...ya gotta be Daddy Warbucks to sling THAT kind of cash around, but hey, my audio needs for great sounding gear takes some long green, but the sacrifice is worth it... 

Fast, dynamic, flow, rhythm all describe several of my amps.