Why should anyone use your free plan without backups? Your service is nothing but liability and vendor lockin. That mentality is why won't even pay for your service. By making backups of premium tier you effectively hold free-tier data hostage through liability.
Once the user becomes invested in the free tier it's impossible to migrate the data out of your service or self architect backing up that data without significant risk with a complicated stack. The whole entire point is to have secure and reliable experience. You need to restructure the free tier to maintain profitability but include backups. Heck you could even limit the free plan with 2 backups
Well you answer yourself - they should not use it for free, they should pay me.
Do you go to a baker and tell him that you want free bread? You know baker cannot even give you free bread and even if it is old and no one would buy it because of regulations...
Free plan is just that you can see what are the options and that you can try it out if it fits your needs. If you want to rely on the service you should pay.
Sorry but by EU regulations where I reside you can always take your data away. You also can take it away each month making essentially what is backup. If I make backups for you, pay.
This makes the free plan less then useless, it makes it a footgun. I'd rather a service offer me a time-limited trial and then cut me off rather than play with my data like that. Someone who's less experienced might disagree and lose their data instead, and isn't that a bad look for everyone involved if it happens.
If you can't afford to offer a viable free plan, don't? If I go to a baker and they offer me free breadcrumbs, they should at least not be mouldy.
Part of evaluating your service is evaluating backup and restore. If that's not robust or reliable, then your service isn't valuable.
If I was paying you to store my backups on a your off-site server. Yes I could see your logic. However, backing in restoring up to my own local hardware incurs zero cost to you.
I'm not above paying for a service the values the end user and their data.
I don't see how it is wrong not to include backups in $0 plan. If you open "Easy panel" pricing page.