“My biggest pet peeve with these types of tests is this: there are a lot of companies out there, and I’m sending out resumes to each one that I can find.”
That’s your first mistake.
Why should a company take you seriously if you don’t take them seriously? Every resume you send out should be custom written and carefully crafted to address their requirements, not yours. Do you do any research into the companies you’re applying to? You should.
Rather than sending out 50 stock resumes, you’d probably be better off picking the top half dozen or so opportunities and do everything you can to stand out. This includes a custom cover letter, follow up emails, thank you notes, etc., whatever it takes to make the connection.
“I simply do not have the time to write fifteen code samples a day, just because you want to evaluate me against your coding test. Period.”
There’s your second mistake. Misdirected attitude. Again, you should be focused on their needs, not yours. If you don’t have time to do 15 poorly, then just do one or two very, very well. No employer or recruiter cares that you’ve chosen a shotgun approach.
Give of yourself without expectations of something in return. You may be surprised at the “unexpected” dividends you’ll reap later.
For what it’s worth: I have conducted over 2500 technical interviews and every single one of them has had to code, regardless of experience or background. What good is a programmer who doesn’t want to code at the one point when it would provide the most benefit to everyone involved? In my experience, the best programmers were the most eager to give it a shot.