Is it worth it? To me, yes! Will it save you time? No! It's a matter of how you want to spend your time. Unless of course you have a physical condition, in which case it's worth it no matter what.
I have Nigerians and it was taking me 10-15 minutes to hand milk each doe. My milking routine took me at least 45 minutes with 3-4 does. I couldn't breed more than that because I wouldn't be able to devote the extra time to milking, so it was limiting my breeding peogram
I got a SimplePulse milking machine and I love it! But it still takes me 45 minutes to an hour to milk. But I'm milking 6-7 does now, and each doe only takes about 2 minutes. The rest is setup and clean up. I keep mine on a cart and I have to wheel it out to the goat pen, set it up, milk, then haul out buckets of water for cleaning, bring the lines and inflations inside, and wheel the machine back to the porch where it's stored. If I had a barn to keep it in and/or hot water out where I milk, it would save me a considerable amount of time. To me, I'd much rather be spending the time moving and feeling like I'm DOING something than sitting at the milking stand slowly slowly milking while my hands cramp. I can do a much more thorough job with the machine. By hand, sometimes I would stop when my hands were tired and my doe was "close enough" but not quite empty. The does also seem to prefer the machine. And first fresheners, omg! There's no more rodeo and milking onto the stand because they're dancing and prancing, and no more spilled buckets! All you have to do is stick the inflations on and keep them held on whole the doe throws her tantrum. They seem to settle into the routine much faster and it is so much less stress than trying to hand milk a first freshener!
So really it comes down to your priorities and your needs. For me it was definitely worth the trade off, but it was an expensive investment and it does not actually save me time. It just makes milking less tedious and allows me to milk more does in the time I'm out milking.