Yes, most employers read cover letters. Or at least read the opening paragraph or two and ski the rest.
Even if they didn’t however, you should still write a solid cover letter for each position you are applying for. There are enough recruiters out there that will read your cover letter closely, especially if your resume ticks all of their boxes.
Most recruiters and hiring managers state that the information they read in cover letters often provides the deciding factor on whether someone gets through to interview or not.
(We are not saying you should ever skimp, however if you are truly time poor, even submitting a basic and brief cover letter could mean the difference between getting an interview and ending up on the don’t call pile).
If you need a hand to whip something up quickly and professionally, check this out: https://recruitablehub.com/get-started/