Some places may accept a title, others will not. Registration is more current - as an example, in MN, our titles are not changed when you change addresses, but the registration does. If you show me a 20 year old title, should I assume that everything on it is current? (Yes, I recognize it is the legal document for ownership, but there is nothing tying it down to current circumstances and matching it to current ID - which is the concern for the storage place - where can they find you when you don't pay the bills or something happens...
Do you get a title on your major appliances? Where the line has been drawn that titles are required is a legal element, not just a it costs a lot argument.
As far as not wanting a place to look junky, there is a big difference between indoor and outdoor storage. Just like anyplace that decides on what they want their facility to look like, there are plenty that don't want cousin eddie's RV in their facility parked outside. Appearances do matter, and enforcing registration and insurance requirements is one way of making sure it doesn't become an issue. If its inside, a lot of this goes away.
And, at the end of the day, its someone else's place of business. Their rules, their insurance (though typically not on your contents), etc... Don't like it? Go elsewhere or lease or buy your own property or building. The rules most outdoor storage facilities here have are very much in line with City requirements for outdoor storage (which includes being operable and registered).