The idea of removing emergency equipment for a 1% boost in gas efficiency is fucking insane, and idiotic.
Not only that, but it's based on flawed logic. 1% weight reduction does not equal 1% gas use reduction. For acceleration - sure! For highway use - no. A large amount of the gas you spend at cruising speed is used to fight air resistance. Guess what doesn't change when you remove your emergency equipment?
So I would love to see some actual numbers, not just some bullshit assertion. It will never happen, of course, because of placebo effect, and because actual numbers take a great many miles to generate.
With all that said, here's the real answer. A matching tire is not necessary. Hell, you can drive on a half-sized spare, you can certainly drive on a full-sized spare. What's important is that it has roughly the same or better maximum characteristics (speed, loading, etc) if you are anywhere near that maximum. For most people's driving, it's not even an issue. Will there be abnormal tread wear? Probably. Will your handling be slightly off? Probably. Will it be enough to really notice? Not really. You may be hardly worse off than the case of 3 used tires + 1 new matching tire (since one assumes a tire pops after you've been driving a bunch, and all four on the ground are somewhat worn.)
In short, it doesn't matter for the distances needed to get to wherever you're going for a while until you can make it to a tire shop to do a replacement. It would matter if you plan to drive thousands of miles, but less for safety, and more for just treadwear and handling.
Necessary, no; needed, only if you plan on using it permanently.