I've seen some stuff here about rootless (3 - 7)jazz left hand chording while the right hand is improvising/playing melody.
I'm assuming this is a general arrangement when playing with a bass.

What is the a general strategy when playing by yourself? Rootless is not acceptable in most cases, is it?

Cover the bass notes as well, play 1 3 7 for instance

Alternate between 1-7 shells and 1-3.

Also, there's stride (root on beat 1 , 3rd and 7th on beat 2)

And arpeggios: 1 5 10 or 1 7 10 or 1 5 9 10, many variations

Yes!

To go a bit more in depth in response to the OP...

You actually can play rootless voicings when you're playing solo piano. It's just one particular flavor though. You probably wouldn't want to use them all the time though....just sparingly.

When I'm playing solo piano and soloing in my R.H. I'll often time play 3 note voicings in my L.H. Root, 3rd, and 7th or Root 7th, and 10th.

I've heard lots of players play these. Oscar Peterson, Bill Evans, Barry Harris, Dr. Billy Taylor, among many others.

Hope this helps.

I have found that a lot of people simply can't reach 1 7 10 voicings.

When the 3,7 or 7,3 voicing sounds a litlle ambigue I add root on the top or somewhere in the middle depending on the position .
To me root sounds less square 5th(exeption m7b5 chords)
And also find the 9th fresh and hip but attention there since it may not fit in all the situations