For years (since the demise of Google Reader) I’ve been using feedly.com (which is free) as the source for my RSS feeds but I never actually use the web client. I use native clients that integrate with Feedly.
For iOS I use Reeder (https://reederapp.com) but for Mac (which Reeder also supports) I use the excellent ReadKit (https://readkitapp.com/).
Most blogs still appear to support RSS but you do get the odd one now and again that doesn’t, but that’s their loss as far as I’m concerned.