The one on the top B and E strings is often needed to give a decent break angle over the nut. The need for one on the D and G strings is debatable.

The need really is driven on a per-neck basis by the string break angles achieved without any string trees fitted. There are various factors affecting this including:

1) Difference in height between the fretboard and the headstock.
2) Thickness of the headstock - which affects the amount the tuner posts protrude from the top of the headstock.
3) Height of the tuner post itself and the position of the string hole/slot. The higher the hole/slot, the less break angle you'll probably end up with.
4) How many string winds you put on the tuner and so how high above the headstock the string leaves the tuner post

The last 3 all affect the height of the string as it leaves the post and so achieved string break angle.

You may also need a larger break angle if your nut slots are shallow with respect to the top of the nut (less that a string's depth) to help stop them popping out when bending strings near the nut.

The top E is always the worst case scenario on a 6-string Fender (unless you use a reversed headstock design), simply through the mechanics of the layout.

All necks are different, and if there is only a small height difference between the headstock and the fretboard, then even with the best height adjustable tuner posts that are pulled as low as they will go for the B and top E strings, you may still not get enough downward pressure on the strings at nut to stop them buzzing on open strings.

If there is a big height difference between the headstock and the fretboard and your strings leave the posts say 2mm above the top of the headstock, then you may get sufficient break angle not to need them.

There's also the question of how high above the fretboard the nut slots are cut. The lower the height, the better action you'll get on the guitar and the easier it is to play strings at the first couple of frets. But if you initially set up the guitar when that distance was greater and with a higher action, and decided that you didn't need any string trees, but then cut the slots deeper (or sanded the base of the nut), then you may find that you now need at least one string tree because the angles have all changed.

How the nut slots are cut can also affect any tendency for string buzz/'sitaring' on open strings. Ideally the slots should slope down slightly from the fretboard side of the nut to the headstock. If they are flat, then with a small break angle, the string can sit on the rear (headstock) edge of the slot and not be pulled down enough so that it also sits firmly on the front edge of the slot, and so vibrated against the top of the slot. Angling the slot can help prevent this if you've got low downward string pressure/small string break angle. It will also reduce the overall amount of friction the nut gives, so helps tuning stability.

I've often removed the D/G string tree on my guitars and filled the screw hole in. I normally leave the the B/E string tree in, but will often change its height so that the string angle is similar to the D and G string angles. No need for them to be greater.