Yeah that's a good example. Say for alpha go for instance. Without the DL network the q learner would be massive. And that's just for a board game. Imagine trying to do that for systems like moving human body parts. Every single body configuration would be a state and then you have every single possible action from each state.
The table becomes unwieldy on much simpler tasks than that.
Consider a 3x3 board where each cell holds 3 bits of information (each cell can be in 2^3 states). Then for the board you have (2^3)^9 = 2^27 different states.
Then multiply that by how many actions you have per state. We'll suppose 9 because you can only change one tile at a time. Then multiply that by 4 bytes assuming we are using a float instead of a double and you get 4.8 gigs of memory for whatever this simple problem is.