Ehhhh. I’m not sure it’s that simple though. I mean, sure, but toss in a water bottle, some foggles (students will forget theirs), an iPad charger, portable battery (cause I’m not trusting an EFB unless I have a backup plan), some paperwork, all the checklists for the three different types of airplanes I may be in, and other one-off items and I definitely need a bag. If I had an office where I could regroup after every flight I would agree. But I’m often stepping out of one airplane and stepping right into the next one... thinking about it, I don’t think I’ve ever seen an instructor simply walk out with a headset, pen, paper, and iPad. Maybe it’s doable though...
Much to do with the experience level of the CFI and the level of the rental place.
Foggles really are standard equipment for a serious rental plane, should have some small sort in the glove box or something, if the students doesn't like those it's on them to bring their preferred flavor.
Checklists, I will not rent a aircraft from someone who doesn't have a checklist in the plane, further more if I don't see a checklist in a plane it would be a serious red flag as to how the aircraft is cared for and what type of yahoo is flying it. A checklist lives in the airplane. I do keep a copy on my iPad for briefing purposes though.
iPad charger/battery, frankly I've not had a fully charged iPad not outlast my max duty day, ofcourse I don't need to leave the screen on all the time no need to.
Plus you should be briefing, debriefing and filling out log books, so tossing your iPad/phone on a charger in the FBO/office/hangar/shack/whatever while you tend to those required duties is a option if needed, if you're just jumping from plane to plane and not briefing/debriefing/filling out the log, you're not doing your duty as a CFI properly. Same with a water bottle, I just never needed to carry one around flying, not even when I was doing full day DZ ops, not like I'm working out or hiking, again between fueling and briefing and log books take a swig of water.
When I did my ATP with ATP Inc (not my first choice) the young CFI had a full on backpack on, like a high schoolers backpack and it was full, of what I have no idea, when we got in the plane I felt like I was flying him to school or something.