2. He'd Make A Brilliant Guide
Should any important visitors come to take a look at UNIT's collection, they couldn't ask for a better guide. Full of wonderment, knowledge and boundless eccentricity,the Fourth Doctor would immediately put most guests at ease and maybe if they're really lucky offer them a jelly baby as he rattled off all the important details. An endless mental database of artists, titles & painting know-how would be ripe for the picking as the man in the hat eagerly showed off his knowledge of some of Earth's greatest treasures & the people who made them possible. Plus a few stories of meetings with them here & there would leave all but the hardest to please audience in raptures. Worth every jelly baby, the payroll people & his UNIT bosses would no doubt agree enthusiastically. On top of that he seems a natural showman. Culture and a little entertainment. What more anyone could ask for we really don't know.