Every generation of DDR memory has increased clock speeds while sacrificing timings. The overall memory latency hasn't changed much because the formula to calculate that is CAS * 2000 / DR or data rate.
Example:
DDR3-1600 CL8 = 10ns
DDR4-3200 CL16 = 10ns
DDR5-6400 CL32 = 10ns
What improves performance is having lower timings at the same speed. Choose the speed for your platform first, then buy the lowest timings your budget allows.
As to how much memory timings affect gaming performance, it's a greater difference at lower resolutions or more CPU dependent games, and less difference at higher resolutions or more GPU dependent games. In other words, if you AAA game @ 4K don't blow the bank on the lowest timing memory you can get. You'd be better off spending that extra money on a beefier graphics card.
The exception to this is if you're gaming on an APU, because then your system memory IS your GPU. Buy the fastest speed, lowest latency memory your system supports.
Ryzen R7 5700X | B550 Gaming X | 2x16GB G.Skill 3600 | Radeon RX 7900XT
Ryzen R7 5700G | B550 Gaming X | 2x8GB G.Skill 4000 | Radeon Vega 8 IGP
Ryzen R5 5600 | B550 Gaming Edge | 4x8GB G.Skill 3600 | Radeon RX 6800XT