If you value living space, you'll be happiest out of NYC.
But if you value meeting a lot of cool people, great things to see and do, great mass transit, etc then NYC is great even at a lesser overall level of purchasing power.
Am I as happy as I was in Boston? No. There's some perks (garage to park my motorcycle and a room for my office) but that's about it. Oh, and things are just easy here. No traffic, the DMV's 'bad' waits are 30 minutes, not 4 hours. That type of thing.
Meeting cool people happens much less frequently here, and the culture (even around OSU) is simply as not as academically focuses as hanging around Cambridge.
Purchasing power way up. Quality of life? A draw at best, probably a loss. If I had my way, I'd be back in Boston tomorrow.
Just taking a rude guess here (sorry if I'm wrong) but it sounds like you might be making a sacrifice for your family or partner? If so, you need to factor in how much they mean to you into your quality of life score for Columbus vs living alone in Boston. (I'm not judging you - a lot of us are in a similar situation!)
Ultimately, it's just not a lifestyle tradeoff most engineering talent seems to want to make at those price points. Upping base to $150k (with something closer to $200k for sr-level talent) for startup engineers (vs ~$100k) would attract more talent the companies are claiming they need. If that's too expensive, perhaps 'startups' should locate themselves closer to where the resources they need are actually located?
Those issues of 'miscommunication' and 'changing priorities' are happening regardless of where the workers are, and I bet many people working at the main office were similarly frustrated.
I've worked on site and remotely, and understand the challenges in each. Neither is perfect, and having a remote team (and being a remote developer) requires certain skills. I'm dismayed, but perhaps not surprised, that these skills aren't actively developed and nurtured at more companies. The long term rewards will be great.