Its not all about logging on and off, that's certainly a super exaggeration. I do occasionally find myself doing the mode switch when looking for Engineer stuff. You know, i know this station will give me a mission for modular terminals, and rather than taking a different mission doing that, and returning, or waiting, or going to a different station, i will simply do the relog to get what i want.
That is a problem, and "fixing" it so that mode switching doesn't work would only lead to further frustration. At the end of the day, if i'm looking to do X, and X requires modular terminals, then i'm damn well wanting modular terminals.
A more difficult fix would be if you could ask at a station if any mission givers will give you modular terminals. If it is possible to get modular terminals at that station then it generates a mission for you (if not it says no missions with this sort of reward is possible), but because they know you value modular terminals highly, it doesn't give any credit or other reward for completion.
A simpler fix would simply to have the mission board update faster. Like every minute. Or have missions on some sort of scroller. I know perhaps FD probably worry about people stacking missions more if it did this. But people already mode switch to stack missions, and all that logging in and out can't be good for the transaction/matchmaking services either. Its hard to change player behaviour or desires, so sometimes you might as well just give them what you want. If mission stacking is a worry, then limit the number of missions of the same type you can have. ie: No more than 5 data delivery missions at once (would also "fix" Sothis a bit)