IMO, the only reason to authenticate with or without slab is resale value. I will submit for authentication if, and only if, the amount I will get for the item is higher than without. Simple in my mind.
To slab or not, I think is more of a personal preference rather than value decision UNLESS you are going for grading, as some might think the slab will be better to preserve the grade. I am sure there are plenty of examples out there of cards ruined by the slab, but the marketing behind slabs and TPAs in general is so successful that many of their faults, including this, gets overlooked by the masses.
Your Cobb check has a very strong autograph. If you think, you could get a really high grade on the auto itself then you would open up the market to a whole group of collectors who only want "the Best" and might be able to charge a significant premium.
You might be able to find the selling price of this one and see if it worth it to pay for the cert
https://www.ebay.com/itm/PSA-DNA-9-E...oAAOSw70xZ4QBC
Here is a PSA 10. It has a lot of watchers, but not sold
https://www.ebay.com/itm/Ty-Cobb-Aut...4AAOSw9L1Zp16e