Thought I'd share my thoughts about this topic.
I started paddling by learning to surf in a white water slalom boat (with rolls and braces), then learnt how to paddle a K1 and then bought a surfski (a Nelo Ocean Ski L).
I was also flirting with the romantic idea of buying a K1 to own long term, but after getting the chance to paddle a couple a really good fast and stable K1 (Vajda Infusion L), I don't even consider it seriously any more.
The good:
1. If you can paddle a K1, any elite surf ski will be doable on flat water.
2. K1 itself only makes sense, if you can push it above 12 km/h for prolonged periods of time. To do that, you will need to increase your physical endurance enormously. For example, to paddle a K1 at 12 km/h for 10 minutes straight, you will have to be able to run 12 km/h for 20 minutes. I know some guys who can paddle at 14 km/h for 30 minutes. They can do the same speed running for AN HOUR!! Speeds below 12 km/h are much more reasonably maintained in a ski.
3. K1s give a different perspective on risk and adrenaline because of the impossibility of remount and usually very low secondary stability. So if you are bored-stable in the most elite skis, then a K1 could be a way to spice things up. I personally am afraid of capsizing far from the shore and thus paddle K1s only very close.
4. You can race in official federation-based competitions in a K1, but as I understand, that's not what you had in mind.
The bad:
1. THE NERVES. When the water is cold or it's windy, a K1 can be a real mind f*ck. And if your technique isn't that great, then it will get even worse with nerves, feedback looping you to that feared capsize.
2. Very limited use. If a surfski can go and do almost anything, the K1 can only do its thing on the flat. There is nothing else.
3. No remounting. Period.
4. Difficult to choose. Skis are usually something you can grow into: buy a much more advance ski, give it time in the bucket and eventually you'll feel confident in it. Buy a K1 a little too advanced and you will NEVER be comfortable in it. So it's very difficult to progress into a more unstable K1, at the same time buying a almost any ski if not to be used in the ocean, can be really a fun idea