My personal experience having used musical children, playing both guitar and piano, electric piano and electric keyboard.
Just to say with a home (electric) piano, it’s important to know that an electric keyboard is fundamentally different to an electric piano, the instrument, amount of keys etc is different, and tuition differs. There are plenty on marketplace, eBay etc but if you’re going to invest you need to research and understand what you’re buying. If you’re going electric, you would ideally get an electric piano with full weighted keys. Not meaning to be patronising at all but you just have to understand the difference.
School music lesson are a bare minimum. They disrupt lessons, the dc hated leaving lessons they were engaged in to go to them, they often don’t gel with the sometimes very strict piece choices of the music teacher, and this is disheartening and demotivating (there are great teachers out there and some dc have great experiences, no offence intended), and at sometimes only 20 minutes long they don’t get too much from them. They have to be supplemented by out of school lessons and at home practise.
If you/they want to be any good and achieve grades they must practise pretty much daily even if just little and often to start ,and learn theory. Some dc who are learning primarily because parents want them to, find this an unenjoyable chore and dealing with this daily can be hard. It’s a seriously big time and financial commitment.
My dc tried various sports, dance, music lessons etc to experience things and find what they liked and enjoyed. It’s important to accept that they might not have a flair for it or enjoy it.
Dd1 started guitar very young, I think she was year 2, and went on to piano and electronic keyboard (as mentioned, different to electric piano). On the whole I would say mine have preferred guitar overall, it’s the instrument they’ve enjoyed and played more through choice. It’s versatile, social, a little more fun and a very portable instrument so don’t write it off.