Well, you should differentiate between 24/7 Remote Monitoring which is what "Pythian" is offering, which usually involves one central number for the customer to call when things go wrong etc. and you get a call "our DB is slow, why is it?"
A small Business which requires an hour of your time per month will pay you quite differently than a F500 Company requiring the same amount of time from you. Now at least here in Europe it is not uncommon that larger than small sized businesses require you to have a certain (limited) company before they would even consider hiring you, no matter how good your experience or price is which in return over here means that unless you can afford 15.000 - 35.000 Euros up front funding your company you will get exactly nowhere. Asides that you might be require to complete certain ISO certifications for your company especially when working in the financial sector. This process takes up to 6 Months before you can have your first review if you would pass or not. I would assume you might face such requirements in the U.S. or elsewhere, too.
So where exactly would be the difference for Company A (in which getting accounts according to your story can take weeks, in 9 years of working with companies up to 200.000+ employees worldwide I've exactly encountered this once that it would take multiple weeks to get access, most agree on a start date with you and do the homework up front) to create an account for you - that would aswell take weeks - or to create the same account with eventually a different name for someone they might hire permanently? What if your desired customers switch to DevOps where the same person does the coding and Administration? Will they kick out the existing DBA, Developer or the external "sometimes watchdog" first? Just trying to give you food for thought if your desired business plan could work out or not.
Asides that I do not see a correlation between going freelance and "main rules" your potential customers might or might not follow through.
My desired customers were in Telco & ISP, tobacco industry, automotive branch and government. I didn't know they were my desired customers, they were the ones offering me the most interesting projects. Today I can safely assume that if you buy an european car you have an 80% chance that your car has at least something from one of my customers, if not multiple customers.
Now I'm not freelancing anymore but I wouldn't mind if my boss had something interesting for me in a branch I haven't been yet. I certainly would find it interesting to design some sort of DWH within aviation or many other things, much more than staying in Telco & ISP (first customer) forever.