Memorizing the cards is the least of your worries in this scenario. It's figuring out when basic strategy differs that is the hard part.
Let's say you're playing a game in which you know the following cards remain: one A, two 2's, two 3's, zero 4's, two 5's, one 6, three 7's, zero 8's, two 9's, and four 10's. You have hard 14 vs. dealer 5, what do you do? (Hit!)
Now let's say that you had one A, two 2's, two 3's, zero 4's, two 5's, one 6, two 7's, one 8, two 9's, and four 10's. Hard 14 vs. dealer 5, what do you do? (Stand!)
Even on a single deck game and 50% penetration, there are approximately 2,500,000,000,000,000 combinations of cards (Sum{n = 1 to 26, C(52,n)}) that can come up. For each one of those combinations, you will have to memorize a basic strategy chart. Even if you say that 99.9% of the hands correlate with a simple count and that 99.9% of the entries (e.g. TT vs. 6) are invariant across different combinations, that's still 2,500,000,000 charts to memorize.
Edit: for a double deck game with 50% penetration, you're looking at 10,000,000,000,000,000,000,000,000,000,000 combinations of cards. For a 4-deck game with 50% penetration, it's 220,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 combinations. For an 8-deck game with 50% penetration, it's 88,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 combinations.