You said, "... they are attempting to make transactions faster..", so no, it is not literally what you said. There is no attempt being made here to speed up transactions, that will always be every 10 minutes +/-.
I see the issue now. You quit reading before you actually read the statement, and instead resort to a false implication of what I was saying rather than taking the extra 2-3 seconds and just reading it. To help spell it out for you:
"(by not having transactions that should be in the first block have to wait 2-3-4 blocks to be added)."
If the current block size can hold 100 transactions and there are 101, they will be put into two blocks. The second one has to come after the first (right? Bitcoin won't let two blocks be filled at the exact same time). The time for a block is 10 minutes. Therefore, one transaction will be forced to wait 10 minutes AFTER the current block.
Increasing block size allows all 101 to enter the first block. Basic math tells us that with an average block time of 10 minutes, the first scenario would result in 20 minutes (avg.) used, while the second would only require 10. To break this down:
Block 1: 10* minutes, 100 transactions
Block 2: 20* minutes, 1 transaction
*time from last block.
According to
WolframAlpha, 10 minutes is less than 20 minutes (click the link, and it will calculate it for you).
Therefore, it has just concluded that increasing the block size will speed up transactions (once the blocks are getting to the point where they are full/overfilled, which is what the increase is in relation to). Because, again, having them all in one block is faster than having them in two blocks. Simple math.
As per my original question, which nobody has really been able to explain (and has nothing to do with any of your replies since you were caught up trying to avoid reading my statement and just making false inferences) is how this is different than halving the block time/rewards and leaving the maximum block size at 1/2 whatever they're going for (10Mb instead of 20), which would ALSO benefit in giving faster transactions while at the same time fixing the original problem.
So far, the reason has been that "Satoshi" didn't make it that way. We've made multiple changes away from how it was originally created, so that's not a reason. It was made as an alpha (which has been stressed over and over for years) and is designed to be altered as needed and as experimenting shows changes are needed. Guess what: Satoshi also didn't set the maximum block size as 20Mb, so maybe we shouldn't do that either, since it wasn't like that in the beginning.
Edit: I also want to state that I'm not necessarily advocating for major changes to the way things work. I'm really just curious as to why what seems like the best solution (and should result in the same thing they're going for BUT also bring more usable applications) isn't the target. There's obviously something I'm missing here.