I've lived in trailer parks my entire adult life, both the mobile home and RV variety, in CA, MI, and NJ (with brief stays in places everywhere in between), 3 different ones in the SF Bay Area (CA).
I've never lived in an actual mobile home though. Too expensive, and not actually "mobile" in a practical sense. Many mobile home parks allow travel trailers or other RV types to rent spaces if they have some spaces without mobile homes in place. (Many others don't).
I've traded up from a 1969 15ft Class B ($1500) to a 1977 26ft Class C ($2500) to a 1995 35ft Travel trailer ($7500), where I am currently writing from right now.
About 250sq ft of non-wall-sharing space, plus covered "porch" small garden, two parking spaces, and 4x8ft storage shed, in one of the most expensive housing markets in the country (SF Bay Area), for about $500 a month, including utilities(!), which I split with my girlfriend.
Perhaps it isn't an option in any of the parks you are looking at, but there are a lot of advantages. Way cheaper (even more than sticker price, since you can more likely buy without a loan and avoid any interest, and tax is based on purchase price). You can move it yourself, anytime, for free. Its extremely easy to set up a solar system. It's appliances are a bit more efficient, since they are designed with dry camping in mind (mobile homes tend to just use regular household appliances).
More than 1/2 my neighbors have pets. I've known a few trailer park residents with large dogs, but I don't know how / why they do it. Indoor cats the park has no reason at all to care, since you own the property they will be living in, but I've had no problems with outdoor cats either so far. My current landlord doesn't especially like pets, but he won't ban them either.
Almost none of my neighbors have fit the trailer trash stereotypes (which, honestly, has been a little disappointing). There was one who had a monster truck, and a couple who did demolition derbies, but the majority have just been random ordinary people, with a wide range of ethnicities, incomes, ages, family sizes, political orientations, etc.
Of all the parks I've lived in (or visited), only one had problems with crime, after new owners took over and stopped doing background checks on applicants and stopped requiring residents to own their own trailer.
Hidden costs - hmmm... Well, there is maintenance on the trailer. Its a whole lot less than for a house, but of course its more than zero, so its more than an apartment or rental house. Some parks charge HOA fees, usually the ones where you buy your space, which wouldn't work for the flexibility you're looking for.
Contrary to popular opinion, I have found heating and cooling costs to be as low or lower. There is a lot less cubic volume of air and stuff to heat or cool. Combine a white roof, tinted windows, a reasonably moderate climate, and tolerance for mild discomfort, and I have not used ANY A/C for 2 years now. Used heat about a half dozen days in the last 2 years (it was a xmas splurge, and then we had the heater out, so we gave in a few times before putting it back in the shed). Most recent electric bill: 77kWh, for $10.21
In summary: none of the objections listed here are consistently valid. In some parks, and with some trailers, yes, but all can be avoided or worked around. Your results may vary.