The Mishna Verurah (136 sk5) writes in the name of the Achronim , Today the Minhag
Is for the Godol Hatzibur (The Rov) to be mesayem the sidrah (takes Achron.)
There might be two reasons for this practice. a) אין המצוה נקראת אלא על מי שגומרה
b) The Rabonim who are Oleh Achron are practicing humility. (Praven Anivus)
For this reason Shishi became a Chashuva Aliyah. Being the Gemoro says that
From Shishi and on everyone may be Oleh, there were Rabonim who were humble
and asked to be called up for Shishi . Eventually it became the Aliya, to
be given to Rabonim.
The Chasam Sofer wrote to R.Bunim Eiger (brother of R.Akiva E.)
He hasn't finalized his contract with the Kehilla of Pressburg
to become their Rov, because, a) They did not offer an increase in salary
for the winter months, to cover the additional expense of firewood.
b) they didn't agree to give him Shlishi every Shabbos.
(They must have settled , & he became Pressburger Rov)