Cheap SAAS? There are existing solutions which offer free tiers but the first paid plan is a steep climb.
Self hosted solutions are pain to maintain. It can only act as good marketing. Its the constant ongoing maintenance & support people are actually paying for.

I myself want a basic log viewing and aggregating system but don't want to pay a lot. Its just about SSH'ing into the server and tailing the file for me. But being able to see live streams of logs in a UI can be cool + alerts functionality.

But before any of that, how are you going to collect logs and send them to your server?