Mt Rushmore was started in 1927. At that time there had only been 30 presidents. 4 where chosen to represent the birth (Washington), growth (Jefferson), development (TR), and preservation (Lincoln) of the nation.
You can use the same motivations if you choose but I think that would be a weird list, too short and not representative of performance on the court or would it even be all players.
Kimball, Calhoun, Donyell, Shabazz for example. Calhoun, Smith, Ray and Ollie could be another. In any case it would surely be an unsatisfying endeavor.
A better way to answer the question given the size of the candidate pool is to fill out a 12 man roster. 2 at each position plus 1 wildcard frontcourt and backcourt player. The coach doesn't require a discussion.
Here's mine:
PG: Walker, Napier
SG: Allen, Gordon
SF: Hamilton, Butler
PF: Donyell, Robinson
C: Okafor, Thabeet
Front: Corny Thompson
Back: Chris Smith
Not chosen due to short tenure: Drummond (center), Henefeld (Front).