360 - Rebuild - Information & Opinions Needed

Some will undoubtedly say it doesn't, and they did it and they had no problems. I'd say if they did and had no problems ignorance is bliss and they aren't attentive enough to notice higher quality in terms of a running engine. If we have to justify a need, I'd say you're probably in that latter group. That's not meant as a cut - there are many things I accept and ignore, and many more I simply am ignorant about and so I'm happy...lol.
IMO, If the pistons are being changed to anything that is not a stock replacement for that year, then yes - it should be balanced. It doesn't matter if it's going into an old ladies grocery getter or a fighter jet. It's not about your feel, but the engine's "feel". Balancing helps to equalize stress any running engine "feels". By doing so it "frees up" power that would otherwise not make it to the crank hub, lengthens the lifespan of all the internal parts, and happens to feel smoother as you drive it.