Would he get the same attention and hype?
And how would that affect his draft status? I remember the last WR we drafted who came in with a father lineage pedigree. Good kid, and the surname helped him some as he knew the NFL game well enough coming in, but the bloodline didn't give him the instinct or desire to go up and fight for a contested catch. Eventually his shortcomings got him a ticket out of town and we got Nacua in his place.
Pedigree ain't everything. Sometimes it helps when it shows through, (Peyton > Archie, CMC > tight end daddy) But not always (Eli < Archie.)
I'm sure the Rams gave the son a solid and objective look in Rice's case, including the intangibles. Already Harrison Jr. is playing the primadonna role. What will Rice do? Stay tuned.