The leader of a community stands as a reflection of the community. This isn't just about heads of state: every leader from tribal chiefs and village mayors up knows that when outsiders look at them as individuals, they are evaluating the community as a whole. Consider what it would say about the US if the President met with foreign dignitaries wearing a Men's Warehouse suit and shoes from Sketchers. Not that there's anything wrong with the Men's Warehouse or Sketchers, but those dignitaries would think "How badly off must the US be that this is the best their President can do?"
Nations, prefectures, states, parishes, municipalities, etc. pay their leaders well (and provide them with stately residences and mansions, limousines, pomp and circumstances, and other formal luxuries) because the community wants their head representative to be respected and to carry an imposing air of dignity, because that will reflect on the community as a whole. When the leader reflects a powerful, respectable, dignified community, that translates to trade and commerce, attracting new business, warding off threats, negotiating new deals, a general sense of prosperous security... Paying a leader well isn't generosity; it's in the community interest.
Of course, some leaders let it go to their heads and abuse the privilege, becoming more concerned with their own (personal) status and power than with the status and power of the community as a whole. Erdogan has been suffering from that in Turkey, Netanyahu in Israel, Putin in Russia, and of course Trump spent his entire life (much less his presidency) trapped in that narcissistic pit. but we shouldn't neglect the principle because of its too-frequent abuses.