Not sure why this is even an issue…
1) Kashrus standards in a restaurant are not the same as in his home (the same would apply to eating at a simcha).
2) To some, eating in a restaurant (other than if one is not home and simply needs food) seems like an overindulgence.
3) To some, it seems slightly unrefined to eat in public, and a rabbi or rosh hayeshiva for practical reasons (for his students to properly accept his words, there should be a certain “awe”) has to maintain his utmost dignity.
Could you see a difference between eating in an upscale establishment and a local pizza shop or burger place?
I’m not agreeing or disagreeing, just hypothesizing.