That's kind of an urban myth, short trips being so bad. Yes your vehicle won't last as many miles but you also won't be putting on nearly as many miles if everything is so nearby.
Short trips are bad is more of a comparison of 3 x 2 mile trips versus 1 x 6 mile trip, while the wear is LESS if you take 1 x 2 mile trip opposed to 1 x 10 mile trip, as long as you keep in mind that the oil change interval should be shorter to account for not cooking off water vapor (or in some modern engines, fuel dilution). The main thing is, you can't then run some lofty high mileage interval between oil changes and instead should stick to a 1-2 year change interval regardless of mileage unless there's practically no miles driven (show car or RV in storage).
My oldest vehicle isn't my daily commuter and I short trip all the time (sometimes just to keep its fluids flowing, sitting too long at a time isn't ideal for vehicles either) and have no ill effects from it, but I only put up to 2 thousand miles on it a year so ultimately it will die from rusting before anything else, because it's also the one I use in the worst of winter, because it's my oldest, lowest value vehicle that sacrifices itself for the good of the rest. Even then, shorter trips mean less exposure to salted roads than if destinations were further away, fewer encounters with other vehicles within that shorter distance to collide with and total it.
Living close to everything you need ROCKS, but isn't a reason to suffer riding a bicycle with the thought that it's bad on a car. If you want to ride a bike and it's safe enough, have at it, but I don't buy the conclusion in the linked article study that we can magically expect a 15% shift to ebike riding instead of cars in any other areas than the one cherry picked for the study.
More likely, we'd have to get 40% of drivers to buy an ebike (which won't happen but anyway if it did...), 35% of them would sit in their garages until they want to joyride so it displaces 5% cars at most and that 5% clogs up roadways (due to the class and wattage restrictions of 28MPH and 750W) by slowing down traffic so the ICE vehicles get worse fuel economy.
IMO it would make more sense for a program with subsidized tiny 4 wheel EV car fleets used as a taxi service, paid for by users just enough to fund the program rather than for-profit. This would make them all weather, capable of speeds slightly past the posted speed limits so no clogging roads, and only enough of them to serve the volume of rides needed rather than a far higher # of them than used simultaneously, like ebikes would be collecting dust in peoples' garages until they want to take a joyride or all ducks are in a row for it to be the right weather, the right roads to the right destination, etc to make sense to take the ebike instead of the car.