Necessary promotion to bishop from an actual computer game:

[Anil]

[d]kr6/P3npp1/1P6/1Qp1P3/2P2n1p/3p4/4r3/1B1R1K2 w - - acd 19/34+; acn 5642827; acs 2; bm axb8=B; ce 32468; pv axb8=B Rf2+ Kxf2 Kxb8 Qd7 Ned5 Qa7+ Kc8 b7+ Kd7;

Maybe not:

[PV] 1. axb8=Q+ Kxb8 2. Qd7 Ned5 3. cxd5 Nxd5 4. Qa7+ Kc8 5. Bxd3 Rxe5 6. Ba6+ Kd8 7. Qc7+ Ke8 8. Bb5+ Kf8 9. Qd8+ Re8 10. Qxe8# Score: MateIn10

Even better:

[PV] 1. Rxd3 Nxd3 2. Bxd3 Rc8 3. Bxe2 Kb7 4. Bf3+ Nc6 5. Bxc6+ Rxc6 6. Qa6+ Kxa6 7. a8=Q+ Kxb6 8. Qa7+ Score: MateIn9

Analysis / Solutions using Chest UCI:

FEN: kr6/P3npp1/1P6/1Qp1P3/2P2n1p/3p4/4r3/1B1R1K2 w - - 0 1

ChestUCI:
8 00:14 5.577.742 534.983 +M8 Bb1xd3
Mate in 8 found ! (1 Solution in 00:25)
8/8 01:28 13.515.664 531.338 +M8 Bb1xd3 Nf4d5 a7xb8Q+ Ka8xb8 c4xd5 Re2f2+ Kf1xf2 c5c4 Qb5e8+ Ne7c8 Bd3f5 Kb8b7 Qe8c6+ Kb7b8 Qc6xc8+

PV= b1d3 f4d5 a7b8q a8b8 c4d5 e2f2 f1f2 c5c4 b5e8 e7c8 d3f5 b8b7 e8c6 b7b8 c6c8

[Anil]

Is there a position which promoting to a rook is required or can I leave the rook out?

Perhaps the oldest and one of the most beautiful:
Saavedra 1895
[d] 8/8/1KP5/3r4/8/8/8/k7 w - - 0 1

1. c7 Rd6+ 2. Kb5 Rd5+ 3. Kb4 Rd4+ 4. Kb3 Rd3+ 5. Kc2 Rd4 6. c8=R!! {6. c8=Q Rc4+! 7. Qxc4 stalemate} Ra4 7. Kb3 1-0

Beautiful game. I guess many engines cannot see the under-promotion to rook. May be that is why we have EGTBs.

[michiguel]

Another:
[d]6r1/k6P/P3R3/8/6p1/6K1/8/8 w - - acd 17/28; acn 36701781; acs 23; bm hxg8=B; ce 32758; pv hxg8=B Kb8 Re7 Kc8 a7 Kd8 Rb7 Kc8 a8=Q#;

Re7+ is better.
After the king moves, take the rook promoting a Queen.

Miguel