I found this ad from Personal Computer World (UK) in 1985. I think we all like their moto! Has anyone heard of this company? They don’t seem to be still around from an internet search I did. But people who worked there may have had an interesting career (hopefully!)
You can do both though. Lots of high-profile software is both open source and available as SaaS.
The beauty of that strategy is you can ensure the software will survive your service provider going bankrupt or otherwise suddenly disappearing, leaving you without a solution.
By not being locked into a specific vendor, competition will be centered around providing the best service, which is in my opinion exactly as it should be.