A blinking light is a warning, in my/any lab. So, it is a violation of safety protocol and a constant source of concern, which requires verification, over and over.
As a side note, almost all laptops I've seen use blinking light (on power LED) to indicate being in sleep/hibernate state. (Then again, some also use blinking light on battery/charge LED for warning, e.g. broken battery.)
I also have some devices that indicate being on by blinking (or more like flashing), but those are low-power battery-powered, so constant LED would use too much energy.
I've also seen devices that use blinking to indicate they are waiting for something ("ready to go/do").
Some routers/switches/modems use blinking light to indicate communication activity, though it is more common to flash the LED based on the activity, so those variants have more rapid and unsteady rate.
I have several battery chargers that indicate the charging status by blinking, some with changing pattern as the charging goes on. Once fully charged, the LED(s) are either continuously on or turned off. One charger indicated failure by continuous red LED (definitely a design flaw, considering red-green blindness).
So the blinking is not universally a warning. But I guess in a lab where warnings are to be taken seriously, there could be different standards to follow. I have only been in labs where the dangers were small enough that blinking wasn't a rule, but in some labs (and whatnot to call them) there was obligatory tour on the emergency shutdown knobs and exits.
The blinking power button when in standby (or "off-but-not-really-off") applies also to at least SDS2000X. Doesn't bother me, I almost always turn the power completely off also with an extension cord that has a switch (or simply unplug the scope). Afaik, at least that 2000X does not need power (at all) to keep the settings.