Possibly, you can run it on paid machines - but why would you? They charge you more for a machine/hour than you can make cryptocurrency/hr.
This is why hosts are often judicious with the free hosting tier - even with address verification and capchas, 60% of the free tier is phishing hosts using a stolen identity and credit card. About 20% are Ebay snipers running shoe-bots, or crypto-miners, begging for bare metal for the response times or hardware, respectively. Another 18% are technology generalists who might cobble together a 2004-era blog hosting service, to engorge their inner nerd - mostly harmless, might not patch something, but will never convert.
For the first 2 groups - once the credit is up (or gets flagged for spam/phishing), the account gets flipped. The scammer uses new email and maybe a new credit card, and migrates their activities. Darknet forums (and probably some subreddits) have lists of providers and how to work the free tier. I expect software to auto-balance between multiple free-tier accounts on multiple cloud providers exists; I've debated scripting the API calls in Powershell in a few weekends.
So people who want them have to get them quick so they need automated scripts that can add to cart, fill in credit info and check out the moment they are released. (The manufacturer usually announces in advance exactly the date and time they will be released).
People pay a lot for these bots. I once wrote a bot for somebody off Craigslist for a certain clothing brand that was selling exclusive jackets and shirts like this. ( I do a lot of automation and scraping for my day to day work so it was not difficult). The guy paid me $600, didn't even try to negotiate downwards. The bot bought 10 items (max allowed in the cart) at like 250 each. I looked the items up on eBay sometime later and they were going for slightly above 1k. So I actually felt I could have asked for much more.
Anyway, long story short, people put a big value on exclusivity and brand so they are willing to go to lengths to secure these limited items.