From the point of view of the draw, I don't think it makes any difference if you're 1 or 2. Unless 1 is always the same half of the draw, which might affect scheduling. I'm not sure if that's the case.
However, I think being world no. 1 is a big thing, myself. It has been slightly devalued in the women's game in the past when a world no.1 existed who had at the time never won a GS event. I'm not sure if that's ever happened in the men's game.
Murray's potential bucket list:
- Wimbledon - ding, ding
- Flushing Meadows - ding
- Davis Cup - ding
- Olympic Gold - ding, ding
- Roland Garros - eeeh uuuh
- Melbourne - eeeh uuuh
- World no. 1 - eeeh uuuh
- GOAT - eeeh uuuh
- $$$$$ - ding ding ding ding
Looking at that list, Murray should throw everything at the AO and FO next year.