The purpose of going to Hojo's old laboratory in Chapter 13 of R1 was due to the context change regarding Aerith's 'capture' by Shinra. Since she went of her own accord in this timeline rather than having been abducted by Tseng (at least, nominally), there's less immediate motivation for Avalanche to rescue her - so seeing Hojo's old experiments under Sector 7 lets them (and, presumably, anyone who didn't play the original) know exactly what's going to happen to her and that a rescue really is necessary. It's also to give Barret and Tifa some time to develop without involving Cloud, though that's a side benefit.
In general, the remake trilogy deliberately runs at a slower pace than the original, taking time to develop areas and characters that were blown through at breakneck speed before. There's benefits and drawbacks to both approaches, and in general I think it's for the better that the remake establishes itself rather than simply trying to be "the original, but better". Especially given that the original is still widely available to buy and play on whatever platform unlike some remakes and reboots.