My eldest two children, 6 and 8 years old, play the piano and the violin and it works well. We accept that piano is their "second" instrument, and therefore gets practised less, however progress hasn't been too bad.
My DD1(8) is due to do grade 2 violin in the summer and grade 2 piano next term. My Ds1 (6), is doing grade 1 violin in the summer and will be working towards grade 1 piano next term too.
I did similarly with DD at that age and regretted it. She started piano as a second instument and made slow progress. Progress in recorder also slowed a lot too but picked up again once she dropped piano. There's only so much time in the day for practice and we found it didn't help to be splitting it two ways at that age.
I don't think it is too early and I don't think you are crazy for considering it, especially since he is already attracted to the piano. I would ask the cello teacher if s/he thinks ds iscready to start a second instrument. IME it seems reasonably common for 6 year olds to play 2 instruments (flute and piano say or violin and piano). I think it would have been too much for my dd
I do think the two together work so well if the child is happy and willing (advice from my musician dad made me push the piano). I think as long as it's a relaxed and fun schedule it's something a 6yr old with genuine musical ability can not only cope with but enjoy.
It's a really personal choice IMHO. My D stopped playing both instruments regularly about two years ago as she explored the things that she found more enjoyable (as well as exam schedule). She still has her cello but rarely plays and we no longer have the piano as it became a very large collector of dust. Nobody else in the house plays and this could have had a bearing upon her enduring interest, or lack thereof.
I know the lessons are really cheap but I think they are just 15 mins. Even so, compared with what I'm paying for the rest of their music it's a bargain. Possibly what's tempting me. Ds2 has said he'd like to learn piano, and I think it will help with cello by supporting his general musicality. But 2 instruments at 6 also seems a bit OTT.
Ds2 has been playing cello for a year and likes having a play around with our piano. He can read bass clef pretty well. His school offer keyboard lessons from y2, when ds2 will be just 6. He's keen to learn but I'm in two minds - I'm sure he'll be in the same place at 9yo if we start now or in y3. I don't relish the thought of supervising practice for 4 instruments as ds1 does a couple too. Otoh lessons at school are relatively cheap (£40 per term) and I think he'd like the piano as it's much easier to get started on than cello. And very logical which will also appeal.
Am I crazy to start him off on piano next September? I think I may be hoping to be dissuaded because my heart says let him do piano next term and my head says wait.