The answer is yes, mass electrification will eventually put some mechanics out of business.
The low-skill places like quick-lube joints will be really hurt. Independent ASE certified shops, and ASE certified chains like Midas will see a slow down, as brake changes will be much less often and exhaust systems will never need work. However, BEVs will still require cooling system repairs, air conditioning work, and suspension fixes.
Tire shops that specialize in tires and suspensions will do fine.
I expect that some independents and many large chains will invest in specialized tools and training, to be able to do BEV specific jobs like battery pack diagnosis/replacements, battery cooling system repairs.
I also expect that in time, a healthy market will develop in after-market high voltage batteries, where you will be able to buy a rebuilt battery pack for a competitive price from a 3rd party supplier, much like you can buy replacement 12v batteries today.
It may be very different, actually, than you expect, because we don't know which alternative fuel technology will win out. If consumers balk at the high cost of BEVs, and we don't have the elusive super-battery breakthrough, then we may see a long term shift to other energy storage forms. For example, we may have a large number of engines running on CNG in the future, as fracking accelerates and the prices continue to drop.
Since CNG engines are still combustion based, that path would have a busy future for today's mechanics.