Paying is not optional, and what you pay for (or not) has consequences
You say the players "avoid paying for it", but paying is not optional. If they do not spend any money on lifestyle, then they are paying for "Wretched" lifestyle.
As the lifestyle section on p. 157 says
Your lifestyle choice can have consequences. Maintaining a wealthy lifestyle might help you make contacts with the rich and powerful, though you run the risk of attracting thieves. Likewise, living frugally might help you avoid criminals, but you are unlikely to make powerful connections.
and for Wretched in particular:
A wretched lifestyle presents abundant dangers. Violence, disease, and hunger follow you wherever you go. Other wretched people covet your armor, weapons, and adventuring gear, which represent a fortune by their standards. You are beneath the notice of most people.
If you want them to feel the downsides of not paying for lifestyle, it is easy to do so: when they are on wretched, most common folk, authorities and certainly any nobles want nothing to do with them, won't answer questions, and will avoid them. Wretched people will try and steal their gear -- time for passive Perception if you do not want to find that purse is gone. Have them roll Con saves each day not to contact filth fever. Violence from thugs or bandits may be a threat on tier one, when such encounters are still a challenge. And so on.
Now, the problem may be that they pay explicitly for lodging, food, clothing and other amenities like baths, instead of a lifestyle choice maintenance fee.
In my opinion, that is not really a problem. The idea of the lifestyle rules is to abstract away time spent on these things to have more time for heroics, but if the group enjoys playing like this, it has the same effect on their funds.
The costs can easily match those of the lifestyle cost table: for example, an aristocratic inn according to the table on p. 158 PHB costs 4 gp a night, and an aristocratic meal costs 2 gp, so with three meals per day you'll get to 10 gp, matching the aristocratic lifestyle baseline cost. They have not yet paid for access to the derby, fine clothes (different ones for every day), perfumes etc.
Shortcutting this with mechanics
You could of course implement a house-rule that states you get negative or positive Charisma modifiers for social interactions in town depending on the lifestyle you pay for, e.g modest has no modifier, each step away gives you −1 or +1, to an extreme for −3 at wretched or +3 at aristocratic.
I personally think this is a bit heavy handed, and it is better handled by the DM roleplaying how people react to them. Effectively, it is not on the players to roleplay that, it is on you, the DM. Of course, it is easy to forget about it, and a crutch like a mechanical modifier will remind you and them of this. But I think it is just that: a crutch, for what you should roleplay to make them feel it.