benefits and drawbacks LLC home purchase?

Benefit: Besides privacy you are protecting your other assets from law suits about that property. For single family, believe real estate taxes are the same with or without llc.
Cost: LLC set up cost in NYC including publishing is $1600 or so. Some small additional paperwork yearly but your accountant can easily do it.

does one simply lose the ability to apply for a STAR abatement for single family in a LLC?

nicesmile yes but I think your talking around $300 a year for the star rebate, its somewhat negligible .
(Unless your talking the senior citizen star rebate, thats a different story.

Mortgages are a bigger deal, especially with current income tax laws, with pros and cons on both sides. 2 off the top of my head that come to mind,
1) Pro for privately owned, no prepayment penalties in most cases, with worst case scenario 1st 3 years of a mortgage only. Not so with LLC
2) Pro for LLC, no $10k a year cap on mortgage interest deduction on your taxes, not so for individual ownership.

For unlimited mortgage deduction, it has to be investment property. Mortgage will need a personal guarantee and may be 10-20 bps higher if used as primary residence with other terms remaining the same.

Appropriately named revocable trust can provide privacy and other benefits while maintaining any eligibility for full-time residence tax treatment. I would explore that option in addition to LLC ownership with trusted tax and/or legal professionals.

Commercial mortgages have higher closing costs, higher rates, may require environmental studies

hmm... higher insurance premiums, no ability to claim the $250k tax benefit per person in the event of a gain during the subsequent sale.

Hey, people here who are knowledgable on this could help me understand this better:

1. you get to deduct MORE interest for LLC primary occupation? I thought you lose the primary resident deduction if you occupy your own LLC property.
2. coops refuse LLC, but are willing to take a trust. WTF? Could someone explain this please?

1) You get to deduct all of it because it is a company owning it so viewed as an investment property. No different than buying a multifamily building.
Owning as an LLC is acting in the same capacity.
Could you imagine multi million commercial properties only being able to deduct $10,000 a year max for their mortgages?
You have to weigh the pros and cons (do the math) on benefits on one over the other. Does it pay more to write off $20k, $30k a year of interest vs the after sale gain of $250K not taxed? etc.

2) Yes, quite simple, an LLC can bypass the board's approval process by selling the LLC to another person. Harder to go after an LLC for delinquent maintenance as well.
You also could fall into financing issues in the building if too many owners are not primary. Banks have a threshold on what percentage of a building can be non owner occupied before they stop giving individual mortgages to new buyers in a building.

Truth on 1. You can’t use as primary residence if declared investment property. For investment property, you have to show rental income or show that you were listing for rent. Once you do that, all expenses are fully deductible. If LLC is used as primary residence, my understanding is that it is treated as pass-through for mortgage interest and income tax but you lose condo/coop abatement for real estate tax.

If you buy with a trust, the idea here is that you'd still be considered primary, because the liability of the trust is entirely of the owner of the trust and the trustee? What if the trust is irrevocable? But the same is true for LLC purchase too, because they'd have to personally guarantee the mortgage, and sign agreements with the condo to personally guarantee the common fees. It's treated as primary ownership for all other legal purposes? But clearly trusts can rent it out as a commercial entity. This is what's confusing to me. What's the legal difference between a trust and an LLC?

Trusts are very complicated and more related to taxation or probate process at death. Some color here.
https://info.legalzoom.com/family-trust-vs-llc-25104.html

Believe it is a costly process to set up a trust.

In my experience, the cost to set up a trust is in the legal fees to get the wording correct so that it "works" correctly for tax and inheritance purposes. Since it's typically part of estate planning package, along with wills and other docs. I don't see it as a costly process. If the financial or control benefits of the trust are justified, how is it costly? (Aside: 2 decades ago my parents spent about $4k in legal fees for all their estate planning (including registering multiple property title changes, etc.) -- they have since separately passed on, and I still manage the trust. It was well worth the expense.)

You can still get it done for 5-7k.

Still, this doesn't answer the question:

according to many (including my realtor), coops treat trust like a person. LLCs are never treated as a person, even when they are guaranteed personally.

Why??? Why do prominent people buy coops with a trust?

Trusts are excellent estate planning vehicles. Beneficiaries are identified and people about whom those creating the trust care. You cannot sell a trust to a third party in the same way you can sell an LLC to a third party. If the LLC owns the shares, all you need to do is sell the LLC and somebody else owns the shares. If a trust owns the shares, there will be no transfer of ownership beyond whomever is identified as the beneficiary of the trust. Note that not all coops allow trusts to be shareholders, but if the board knows all the parties involved (specifically the named beneficiaries), then the the board is more likely to approve transfer of ownership to a trust.

Trusts can be complicated, but as pertaining to co-ops, lets look at co-ops in general.

Co-ops
1) Prefer primary users.
A trust mostly satisfies this. As most co-ops have forms of allowances for family members to live in the home, a trust generally is about transferring or sharing assets with family members.

2) Don't like rentals.
While a trust theoretically could lease out an apartment, the co-op's bylaws would supersede that as the trust would have signed a house rules agreement and be beholden to the co-ops rental policy, if any. An LLC can be sold to another party and bypass this. A trust will likely have more assets than an LLC as well.

3) Attract an older generation of buyers.
As people get older, to most, having some control over who are your neighbors is preferred, and dont like high turnover, etc. Trusts are also something that older people form so fellow co-op'ers are amenable to trusts as they require them themselves.