Leaving the printer on all the time avoids triggering a maintenance cycle each time you use the printer. When we did that with some of the most ink-hogging models, it did noticeably reduce ink consumption. Canon told us that "if the printer is switched off then it may do a longer clean."
Worried about the cost and environmental impact of the extra energy consumed? Inkjets left on consume very little power when not in use, so your ink savings should considerably outweigh the energy cost. https://www.consumerreports.org/cro/magazine/2013/08/the-high-cost-of-wasted-printer-ink/index.htm