Some shuls have ritual committees who set rules (in consultation or subject to review by the Rav). Our shul set rules that deal with this more than 20 years ago and when we interview new candidates for the position of Rav they are provided with them.
Membership (meaning PAID up to date) has its privilege. If there are 2 men wishing to daven for the amud in the same need to say kaddish standard, the fully paid up member gets the honor. He may choose to relinquish it to a guest, but is not required to do so.
It costs money to pay utilities, insurance, salaries, etc. That doesn’t come from the money a guest might stick in the pushke, it comes from dues and annual pledges.
I know when my father’s Yahrzeit is, when I show up and there is no one in shiva or shloshim, I expect that I or my brothers will daven for the amud. There is no other male member of our shul with the same yahrzeit. My father’s memorial placque will be lit and one of us will be at the amud. Generally, my eldest brother davens Maariv and I davem Shacharis. We provide a breakfast after minyan. We leave Mincha for any member who may be in the mourning year, or a guest if there is one in need. Otherwise, we let a remaining brother daven.