What instrument to encourage your student to play is definitely worth some consideration as it can certainly have an influence on your childs relationship with music.
Ultimately the answer is that you should be encouraging your child to persue the instrument which excites them the most. A student enjoying their instrument will be more commited, more willing to practice and more attentive to a teacher. It's also very important to note that most instruments now have an electronic variant which can be play directly through headphones, so there's no need to be scared off by your childs instrument choice being a loud one.
The tricky part of making this decision of course can come when a child doesn't yet have a clear idea of what instrument they're interested in, which is incredibly common. Our school is more than happy to accomodate these beginners, offering starter packs which can be used to try various instruments. This way the student can have real hands on experience and guidance from teachers before deciding which instrument to stick with. You can find more info on that here.
There's also many behavioural indicators to lookout for, especially in very young children that may hint towards what instrument might be the best suit.
Do they tap their hands and feet all the time trying to make a tune? Then drums might be the answer.
Do they jump around playing air guitar? Well then guitar is probably the best suited instrument.
Do they sing along to all their favourite songs? Then singing or perhaps even piano might be a good fit.
And of course consider what instruments are prominent in the music your child listens to.
Most importantly, always keep in mind that changing from one instrument to another is never a waste of time, skills developed on one instrument will make the next instrument easier to learn and help provide a good all round knowledge of music. So for anyone starting on one instrument and wanting to change to another, feel free to, it might be the best decision you make!