Normally WiFi devices don’t sleep (it’s one of the things that makes them go through batteries so quickly). You’re definitely right that if that particular brand has been engineered to sleep, re-connecting to the network every time it wakes up will add noticeable lag.
Zigbee and zwave battery-operated devices typically don’t have that issue because they don’t have to go through a rejoin process after they sleep. (Although the devices that also get moved around physically like handheld remotes may have to find new neighbors if they’ve been moved to a new location, but that’s still faster than a network rejoin.)
I did notice recently about a dozen Wi-Fi battery operated sensors, all from the same factory, in the coolcam design, all using the Tuya or Smart Life app. It looks like they are intended for the Amazon Echo market, but the ratings are pretty uniformly abysmal, as opposed to the few that appear to have been designed independently for Wi-Fi.
The unacceptable ones are also using the same small cases and the same small batteries that zigbee ones from the same factory use.
The Wi-Fi sensors that were designed from the beginning for Wi-Fi tend to have much larger cases and use at least three AA batteries. They are discussed in the wiki article.
So I suspect your experience was pretty typical with the small ones, regardless of brand.