Well since "should" is a value judgement that's going to depend on an individual's (or community's) goal.
For my goal, a slightly non-neutral amplifier fits the bill (my tube amps). Why? Because I like the
warmer sound.
Which brings up the question of whether it should be decided for everyone what they have available to buy for their own good; and then who should decide that.
Personally, I spend all my spare time at grocery stores knocking ice cream toppings out of people's hands; because if they had meant for you to have chocolate with it they would have included it in the ice cream!
I haven't been able to decide what annoys the objectivists the most, that equipment that doesn't fit their desires is made, that there are people that buy it or that there are people that have the nerve to like it better than the equipment the objectivist prefers.
One of the biggest problems that I have with the use of the word "warm" is that a Google search will come back telling you that it means "thumpy bass" or therefore colored sound. I have always felt that the equipment should not color the sound. If an end user wants "colored sound" then that is what tone controls or an EQ are for. So that the end user can do the coloring. Who wants color baked in? Not me. I want neutrality and then I can go from there.
So, then buy equipment without it and add an EQ. What I don't get is why everyone has to want exactly what you want. Thread after thread here makes fun of people that make, buy and listen to amps that aren't what the large percentage of members here want. Yet there are plenty of options that suit your desired needs. If I have an amp that suits my room, my speakers and my listening position and my preferences without any additional equipment or settings required then why wouldn't that be the perfect amp for me.
And I have never heard of warm sound described as thumpy bass, I guess I don't go to google for my definitions. And that is the root problem of every argument about a subjective term. To me, the bad side of warm sound is lacking high frequency sound levels; but the good side is strong midrange while still holding onto the high end detail.