It's one of my pet hates, and people who like villagers based on what is popular & "OMG KAWAIIIIIiiii TIER 1 lalalalala..." (usually with even worse spelling & grammar. Maybe something that resembles text-speak...) usually aren't that great at having meaningful conversations anyway....
So I guess it acts as a helpful filter & warning system! Like what one of the commenters said above about people who pick up an ugly purse that they wouldn't normally like...but they do now it has a brand label stuck on it...they think it's a form of prestige.
My town is a mixture of whoever I really like. Some I was surprised were actually quite popular, (like Marina, I really wanted her & was shocked she was so popular! I thought a pink octopus would be considered "weird" but there you go!)
My villagers are Wart Jr & Keaton--Tier 5
Tangy, Phoebe & Muffy--Tier 2 or 3
Lobo--not sure of his tier, i think he's a 3-4? I know he's not as popular as many wolves, same with Freya--my favourite snooty.
Kid Cat--I think he's actually Tier 1 or maybe 2? I know he's very popular, but I just love him because he's quirky & cute.
I also have Colton who seems to be popular, but I can't stand him and want to replace him with Stitches--a big tier 1, but I love him because like everyone else--he reminds you of your beloved childhood bear--so that makes sense & he's in a lot of hearts.
So as you can see I have villagers from all the Tiers & they are all my best friends that I never want to leave (except Colton!) and I've also had high tier ones I found boring and had leave--such as Chief & Zucker.
It's a shame the tier system means some of my picks for my second town like Annalisa, Amelia etc will be harder to find due to "autovoiding" and that word alone sounds sociopathic to me!

NOT GOING TO MAKE ME ANY BELLS??? AREN'T POPULAR ENOUGH?? FINE, TO THE VOID WITH YOU!
When the tier system did influence me was when I had a cycle town, knowing when I was being duped or not--because it is annoying to have someone offer another seller a crazy 15 mill bells for a tier 1... and then try to argue with you... "thanks" (sarcastic thanks) to the tier system it gave villagers a bell worth, and you need to stick to it for consistency.
I'd rather have set equal prices, but then seeing them give more bells to someone else did make me feel bad about myself & want to charge the same.
I did however try to even things out by holding onto the lower tiers for as many days as the higher tiers.
- - - Post Merge - - -
Also thanks for asking this question, as in some ways it's brave to question the tier system--as so many people are likely to become defensive & not want to admit that they do want to chose the most popular villagers.
I was happy to see that most of the votes & comments are actually just as unhappy with the tier system as you.