It doesn't meaningfully make you "more independent" because all Relays are trivial (they're just dumb re-broadcasters of a stream) and it makes sense to use one run by somebody else — a company or a community that's pooling resources.
Say if Bluesky (the company) bans someone, that person could still have the keys to their data, but their feeds will no longer be "re-broadcast" by that company's servers - right?
If an app is concerned that a relay is censoring some user that they care about, the easiest solution is just to host their own relay. It's probably cheaper to operate than their app is. But if they really wanted to, they could listen to multiple relays to "cover the gap" or just manually listen to the event stream from specific users' PDSs directly whenever they notice censorship (effectively operating a partial relay in addition to listening to a full but censored one). But, again, in reality they'd just host their own relay and not bother complicating things.
The hardest problem of relays censoring content is to notice it happening, but once you notice you can easily verify it and switch to a different relay.
It's less like a cellular plan and more like building your own private cell tower just because you can.
$30/mo is $360/yr, which for most people is a prohibitively large sum of money. That would make Bluesky access more expensive than even the most expensive Netflix subscription; closer to the cost of a cellular plan.
For comparison: for my Mastodon account I pay $5/mo or $60/yr to a dedicated hosting provider. This puts it in the same ballpark as paying for a private email host or a VPN subscription.