Is this theory or practice?
People who individually craft CVs and cover letters (I do) go through a very resource consuming process.
Having all the CVs and cover letters externally reviewed makes the process even more resource consuming.
It's crucial to differentiate spell-checking from proofreading.
The parent specified spell-checking; there is a reason to be strict on this, and it's that spell-checking a document takes less than a minute with a word processor, so one really needs to be careless to leave more than a couple of spelling mistakes.
Proofreading on the other hand, is much more demanding (finding people, coordinating, reviewing and applying changes), and often, gives feedback that may not be very useful or even conflictual between reviewers.
I don't think proofreading for more than a handful of CVs/CLs is realistic (expect for the CV-maniacs).
I wouldn't want anyone to pay for a resume review because the advice you get from that can be quackery or even conflict with other articles about resume writing (apart from 'no typos', they can pretty much agree on that).
Really, the point was if you're going to use a superficial filter like that, you may as well automate it to something like a code test so you can save yourself even something as small as 10 seconds x N resumes per year.
And yes, I consider that it's difficult to write correct English. But if you're willing to send out an erroneous resume without getting it competently reviewed, I have to suspect the depth of your commitment to quality overall.