Try going for a run along a pavement with frequent curb cuts, it's not pleasant. UK dropped curbs are somewhat less of a trip hazard but are so frequent in towns that you end up running with an ankle at an angle.
One "weird" complaint that I have with some accessibility features is that they mount things so that wheelchair users (and children) can operate them, e.g. a ATM mounted at groin height. I'm fairly tall so now I struggle to operate them or have to bend in unnatural angles. It's a small price to pay to make the world navigable to others, but almost daily I run into things that "are clearly designed by idiots". That is until I remember that the average person is below 180cm and right handed.
Even if this is not the case for some weird reason - don't you agree that making the world a little bit more accessible for people who have a really hard time getting around is worth making the world just a tiny little bit less accessible for you - the person who can litterally run around?
If you have a considerable problem with tripping often though, maybe look at how you do running.
My most unpleasant experience so far has been during my daily public heavy deadlifting routine. When I place my barbell on the edge of the curb, which my particular style of lifting requires, it's placed at an angle so my back got messed up and it's all the fault of these curb cutting measures.
It's all fine and dandy you want to assist children and handicapped people, but it'll be at the expense of regular users of the pavement which use it for completely sane and normal activities.
Just make sure you alternate which side of the road you are running on somewhat evenly so you are getting the benefit on both sides.
My conclusion, as always, is that U.S.-Americans and Brits do not walk. Otherwise these design choices do not make any sense.