Wye or Delta, Source Side Power Generation and Distribution

Let me add some information to this part of your question

"from my understanding, if you choose wye instead of delta, then the power produced will be increaced by a factor of the root of 3

in addition, if the load is designed so that it is in a delta instead of wye, the power available will again be increaced by a factor of the root of 3 "

in wye connection V (line to line) = 1.732 (Vline to neutral) while I(line) equals to I ( phase)
But in delta V(line to ilne) = V( phase ) and I (line ) equals to 1.732 I (phase).

In both cases the power is the same. Please note that now changing from wye to delta or vise versa will not increase or decrease the amount of power.

It is not important to always be wye to delta. There many types of connection such as delta to delta, delta to wye, wye to delta, wye to wye.

But wye connection is always used for distribution because

Ground exists in this system and it is more safer.
It has neutral and it is good for unbalance load because it is not possible to make load 100% balance.

For Delta
Good for balanced load
This system is ungrouded means there is no ground conductor and it has many its own usages.

I'd like to add that Delta-connected power has quite a few advantages over Wye-connected power, however system voltage can be compromised. It is not true that all sources are Wye connected. Some utilities supply delta power practically to their entire grid (Los Angeles for example) With a Delta, if one phase is lost, the system will become an open delta and overall bank capacity will be reduced by 57%, however line service should not be interrupted. If there is a drop in voltage on one phase of a Delta, it will cause the other two phase voltages to raise as the source coils are in series. This makes regulation a problem should a fault or leakage occur. It is possible to ground a Delta, but not individually on each phase as a Wye connection would be.

tyvm :)