Colin Fletcher used to say, "This is still an honest industry; you get what you pay for." He's still mostly right (with a couple of minor exceptions.)

When it comes to tents, you may choose two: light, cheap, weatherproof. You can't get all three.

The major flaw in your reasoning is "assuming summer use." However, if you are only going to use the tent in clear, hot weather, or can crawl into the car to sleep if it happens to rain, I still don't think a cheap tent is worthwhile. In those conditions, I'd submit that no tent is needed - just take a groundcloth and sleep under the stars (and maybe some bug netting to hang if bugs are an issue.)

Way back when, I bought one of those cheap Texsport single wall pup tents. It was hot when dry, wet when it rained, and cramped always. I soon went to a 6x8 coated nylon tarp and a piece of Visqueen, and found it far superior (I hung one of those twin-bed sized mosquito nets in it during summer.)

By the way, my choose-two selections are light and weatherproof.