The upshot is that a ten speed cog will wear about twice as fast as a BMX cog. The chains themselves, on new cogs, will wear internally at the bushings and pins, based on the quality of the chain. But since the narrower cogs wear faster, this will indirectly accelerate chain wear.
I have said this too many times. Somebody needs to produce a drive-train for high powered (over 750 watt) mid-drive bikes. A five speed cassette with cogs and spacers twice as wide as ten speed, wider idler spacers for the dérailleur, and a shifter with every other detent missing/filled to use BMX chain.
A 14-42 cassette gives nice even spacing, a 3:1 or 300% or 8-24 mph range (however you want to think about it), and a minimum of seven teeth engaged.
Traditional chains with bushings have a lot more projected area in the bushing-to-pin interface, so they last a lot longer in single speed applications with good sprocket alignment, like track bikes or industrial equipment. You have to lube them through the gap between sideplates, which is sometimes tricky. That is one reason that they invented thin oil.
Modern ramped cogs would make that chain shift even better. Cog center-to-center spacing on those bikes was 5.5 mm. The center-to-center spacing of 5 cogs on a current cassette would be 7.9 mm. A chain as stiff as rebar would work with that much space.
A narrower sprocket leaves more room for a 1/8" chain to deflect sideways before contacting the adjacent sprocket. So a wider sprocket isn't necessarily an advantage.
What is chain suck? The chain will try to cling to the sprockets causing the whole drive to bunch up and crash the bike. So it really is good to keep the chain very well lubricated.