Set, showed and sold are three separate rates with three separate causes
A dealer reporting one conversion number cannot tell a phone problem from a scheduling problem from a selling problem.
The set rate is how many inquiries turn into a booked appointment. It is a phone and follow-up question, and it responds to speed, persistence and who is doing the calling.
The show rate is how many booked appointments actually happen with the right people present. It is a confirmation and expectation question, and it has almost nothing to do with sales skill.
The close rate is how many consultations produce a signed contract. It is the one everybody watches and frequently the one that is fine.
Averaged together, a dealer with an excellent sales team and a poor show rate looks the same as one with the reverse, and they need opposite interventions. Hiring a better closer will not fix a confirmation problem.
Splitting them costs nothing but bookkeeping and it is usually where the surprise is. Most dealers who do it for the first time find that their weakest number is not the one they had been working on.