If we're talking about using the batteries for propulsion (and we're talking about aircraft that can carry at least one person) then it boils down to, in a word, weight, or in two words energy density. Li-ion batteries have a pretty good energy density for a battery, but they aren't even in the same league as aviation fuel. Heck, they aren't even playing the same sport.
Something like Avgas has a Specific Energy of ~44.65 MJ/kg, Jet fuel ~43.15 MJ/kg and at the moment Li-ion batteries as used in electric road vehicles are around 0.72 MJ/kg so for the same take-off weight you're going to get a frankly pitiful amount of range.
That's not to say it isn't being looked in to - e.g. Vertical Aerospace's proposed
This paper does some modelling around the concept of an e-VTOL aircraft like the VA-1X, and for a Gross Take Off Mass of 2500kg (about the same as a fully laden Cessna 172) you get less than a hundred miles of range. And that's when the batteries are new - once you start putting charge cycles on them the figure is only going to drop (no pun intended).
The weight of the batteries needed to replicate the range/performance of even a modest passenger jet is mind-bogglingly huge.
Of course that doesn't mean we'll never see battery-powered aircraft - Tesla have been teasing a substantial step in pack energy density for a couple of years now, and an alternative battery chemistry of Lithium-Sulfur (Li-S) offers a potential solution as they're already hitting nearly double the energy density of Li-ion (and improving rapidly) and if they can solve or mitigate the current issues Li-S has with rapid degradation and power-to-volume ratio then they could be very promising.
Texas aircraft are working on a Li-S-powered electric version of the Colt that could have a range of around 200 nautical miles