What do I lose?

If I set my bevel at 1k, and I can usually set a pretty smooth bevel, what do I lose if I skip my 6000 and go right to polishing that bevel? I've done it several times lately; spending a little more time with a slurried 12k rather than mess with the 6k. Honestly, I think I tend to not improve by edges much at all on the intermediate hone.

I don't want to be SRP heretic, maybe I just need a better intermediate stone than my King 6000?

I have King 6k and i think it is a good stone. I used to go 1k, 3k, 6k, 12k until my 1/3k King decided to stop our teamwork and crack in two, so nowadays i do 1k (Norton), 4k (Norton), 6k (King), Coti, 12k.
If you get straight from 1k to 12k, you will spend a lot of time polishing that bevel. Not that it can't be done.

you will loose time a lot of it.

While he is referring to plane irons in the quote below, Harellson Stanley, of Shapton USA, knows something about stones and sharpening in general. IME intermediate grits are the only way to go for best results. If you are getting adequate shaves with what you are doing that is fine but my guess is you would have far better edges with a stone in between the 1 and the 6k. Here is what Harellson says,"When I have reached a consistency with one stone then I move to a finer one to remove the scratches from the last. The tool should, after the first stone be looking as nearly perfect in shape as possible, it is very inefficient to try to reshape a tool with the next finer stone. When I'm sharpening a plane iron, I often go back to the beginning to reshape, as with all buildings, a proper foundation is essential. The front corner is still not right, back to the starting line."

What are the rest of the hones in your setup? I've never used a King 6k, so I can't compare it to anything else, but if you don't like that one, maybe try another hone in the same range. There will be a few varieties available at the WNY meet, or if you want to try sooner, drop me a PM and you can play with my Naniwas.