Another thing I was thinking about is if you are going to build a settler at size 3 and only get a 1 pop whip, you may as well get bw early and get in a whip at 2 pop.
Whipping is a complex case-by-case subject, but suffice it to say this isn't efficient.
If you whip at 2 for one population, you're left with a 1 pop capitol to start all over. If you are improving tiles with your worker like you should be, you'll just be waiting on regrowth before working them again, slowing your relative progress as the city can't contribute again for more time.
Whipping at 3 can be better as it leaves a bigger city, but the time saved is minimal or even nothing (if you can't get to BW + whip threshold of 70/100 before the settler would just complete anyway) but you gain an unhappy penalty and little overflow for nothing but a time save. Maybe.
There's also less overflow from 1 pop whips in addition to having to wait longer to meet the whip threshold. 2 pop whipping at size 4 can be done as early as 40/100 on the settler, which makes up for some of the time spent growing to 4, and leaves you with a size 2 city again. You also have the option to put more progress into the settler which delays it, but allows overflow hammers to be put into something else immediately after the whip, when regrowing or just to more efficiently use your tiles on other workers/settlers (essentially turning food into hammers on them through whip + overflow).
The timing of BW is such that it's usually not saving much time on the first settler to whip it, and even if it does, repeatedly whipping that way as fast as you can might cripple the city with unhappiness quickly too. Unless the tiles you're working at size 3 are very strong, you also risk delaying the 2nd settler/worker too if you whip the first settler, and so on. It's a complex relationship and I admit that I mostly feel it out myself rather than really crunch numbers, but it's important to have a sense of the interaction between slow building and whipping.
There are many scenarios where it can or can't be a good idea to whip, slow build, or chop at a particular size. It depends heavily on the start and how you're able to manage it with the played civ what works best, or certain gambits you may wish to undertake can dictate speed over efficiency (I NEED to take land ASAP) etc.