If the original question is asking do grading companies set a minimum, I believe the answer is no - they will take your money to grade any acceptible card. It's always a gamble when it comes to knowing the right time is to slab, hold, or, sell.
I noticed yesterday that PSA has 'suspended' their $20 economy level service - forcing you to either go for the higher rate of $50, or join the Collectors Club to get the $10 rate. Oh but, they are also 'sold out' on their Gold and Platinum Collectors Club, so you need to join the Silver level, where you recieve zero vouchers for your $59.
Please visit my YouTube channel 'The Vintage Composer' for more info on sports card collecting, sports history, trivia, and more!
https://www.youtube.com/channel/UCPoAYGOXYlY9OBIZPKqsCgA/videos