Uber in the UK must be awfully cheap?
Six trips a week (round trip makes 12) plus a few far-away competitions, so at least ~50 trips a month. For 400GBP?
I rarely use Lyft/Uber but even the shortest trips I've made (just a few miles) are at least $30.
Most of his trips would be to local leisure centres within about a two mile radius that would have been walkable in 20m-40m if not for the lack of time to finish up work, get him ready after school etc.. Normally I'd prefer to walk, and that's a large part of the reason my transport costs are very low.
EDIT: Just checked my most recent few trips, and I paid 16 pounds for a trip Google Maps tells me is 7.4 miles driving distance, and 20 pounds for the return the same distance. The last few trips to my local station have been between 6.50 and 8 pounds, so definitely gone up.
Even when my son was swimming competitively and we had to Uber him around to 6 training sessions a week plus often competitions many miles away, I only briefly averaged 400GBP/month in total transport costs (though with the caveat that I work from home; had I commuted full time it'd have added ~200/month to get in to the centre of London, but then again I'd likely have spent that even if I had a car because commuting in to the centre with a car is a nightmare)
And I got to sit and relax and read or talk to my son or listen to music and not have to pay attention to the road.
I get that some enjoy the actual act of driving and/or driving a comfy, fancy car, but for many, it's a really expensive enjoyment and I suspect a lot of people have not considered just how much they could "paper over" edge cases and issues with public transport (yes, I know this is not a viable options for huge parts of the US) or choices like yours with Uber or rentals.