Titles are a tricky topic. Some people don't care about them at all, others care deeply. Most people are somewhere in the middle and do like a title bump once in a while to show career progression.
Plus, titles are not just for internal consumption. Titles help you quickly describe what you do to someone that doesn't work with you; and ultimately it's what you put on your CV.
So titles serve a purpose; but they are also a bit of a litmus test for a company's culture. If people are getting seriously worked up about titles, there's a fair chance they're actually upset about bigger things.
One trick I like for companies that do business cards: don't let anyone put their title on a card. Just name, company and contact details. It's not just a way to avoid reprinting cards when someone gets a new title, it's a nice equaliser.