I believe OP is referring to input latency, which isn't so much a result of the system slowing down due to increased load, as much as running in a consistently slowed-down state causing a delay on your inputs being reflected on-screen. There's several reasons for why this is happening more often lately.

Part of it has to do with the displays we use nowadays. In the past, most players used a CRT TV/monitor to play games, which have famously fast response times (the time between receiving the video signal and rendering that signal on the screen is nearly zero). But modern displays, while having a much crisper picture, often tend to be slower at the act of actually firing pixels on the screen, causing that delay between pressing Jump and seeing your character begin jumping.

Some games also strain their systems so hard that, after various layers of post-processing effects get applied to every rendered frame, the displayed frames are already "old" before they're even sent down the HDMI cable, resulting in a laggier feel for the player. You'll see this difference in action with games that have a toggle for a "performance/quality" mode in the graphics settings. Usually this setting will enable/disable certain visual effects, reducing the load on the system and allowing your inputs to be registered faster.