> many of the simpler DNS tools -...- do not support API control
That's on the DNS provider in my opinion. They can, if they want to, make things easy and automatic for their customers, but they choose not to. There's a whole list of provider-specific plugins (https://eff-certbot.readthedocs.io/en/stable/using.html#dns-...) with many more unofficial ones available (https://pypi.org/search/?q=certbot-dns-*). Generic ones, like the DirectAdmin one, will work for many web hosts that don't have their own APIs.
If you like to stick with whatever domain provider you picked and still want to use Let's Encrypt DNS validation, you can create a CNAME to another domain on a domain provider that does have API control. For instance, you could grab one of those free webhosting domains (rjst01.weirdfreewebhostthatputsadsinyourhtml.biz) with DirectAdmin access, create a TXT record there, and CNAME the real domain to that free web host. Janky, but it'll let you keep using the bespoke, API-less registrar.
I imagine you could set up a small DNS service offering this kind of DNS access for a modest fee ($1 per year?) just to host API-controllable CNAME DNS validation records. Then again, most of the time the people picking weird, browser-only domain registrars do so because it allows them to save a buck, so unless it's free the service will probably not see much use.