I have thought about the same thing. I'm still looking into it myself. What attracted me to it was removing my primary residence out of my personal name to make them harder to access if someone sues me personally, assuming it is setup properly. This is something I haven't fully settled myself, but from the research I have done so far going with an LLC for that Holding Company may have drawbacks in regards it its ability to be pierced (ie. vs. a properly structured LP). You should seek professional council from an asset protection attorney (and if you find a good one let me know as I am seeking one myself).
I think the other benefit is expanding the items you might be able to write-off. This should include repairs and maintenance and things like that but also depreciation. I have converted my personal residence into a rental before but I'm not sure if there are any special rules if you then rent it to yourself or if there are any complications with things like depreciation related to the way you are likely to want to transfer it into your holding company (ie. what is basis if you just transfer in with no real money changing hands due wanting to avoid significant exchange and related taxable event). Perhaps someone else has some more knowledge there.
I don't know if you have kids, but there may be an impact on financial aid if you do this. Most financial aid will give some level of exemption for your primary residence and not consider it. There is usually some cap to this (ie. 2.5x your income or something like that). Moving it into your owned company would then make it a business asset I would think. Now, the FAFSA excludes majority owned small business assets too but CSS Profile does not. In FAFSA case though you need to really make sure you run it as a business because in most cases it tries to consider real estate, regardless of how it is owned, as a personal asset, but I have read you might be able to avoid that if you can show it truly is a part of a real business.
Downsides would be you would lose STAR exemption (NY reduction in property taxes for primary residence) and the above mentioned exemption for financial aid. I believe there is also some level of exemption of a portion of your primary residence in a lawsuit. I believe it's called the Homestead Exemption, but that depending on the state, it is often not that much. There are certainly complications with changing title if you still have a mortgage on the property as well and you would need to make sure doing so wouldn't trigger the due-on-sale clause you likely have in your loan.
Again, I'm no expert on this, just sharing what I have gleaned from my own research on the subject as I have explored the same question. Interested in whatever advice others might have.