Not in my experience. Have had one for several years, switch it on when I need and turn off for weeks at a time. Runs perfectly and total cost of ownership is already lower than the mid-range pro HP printer I had before.
Also laser printers draw a lot of power constantly, you may be confused here. The toner needs to be kept warm.
The problem for GP and for me too is inkjets needs a couples of cleaning and test prints after a drop of IPA on K, C, LC, LM and M ink drawing port each time I'd use it. That won't happen with lasers at all.
It has the problem the GP was talking about, increased to complete new levels.