The main purpose of an LLC is to provide liability shield, and complex distribution of ownership vs management rights, without the tax complexities and "double taxation" of a corporation.
The IRS won't even see it
When you form an LLC, it assumes pass-through tax treatment by default. It's possible to elect corporate tax treatment, in which case the LLC files its very own Form 1120 every year, but that's pretty unusual, for obvious reasons.
"Pass-through" means LLC assets, gains, debts and losses are simply treated as those of the individual Members and pass through to their individual 1040 tax forms.
A "Single Member LLC" or "SMLLC" is a little more special. With only one Member, and pass-thru tax treatment, there is only one 1040 tax form involved. At this point, the IRS calls the LLC a Disregarded Entity.
With an SMLLC, thus, IRS simply treats all LLC assets, income, debt and expenses as your personal items. Selling your real estate to the LLC would be a non-transaction in the IRS's eyes. They wouldn't care what value the SMLLC carries on its books, since it's the same books. When the LLC finally sells the property, its cost basis would be what you originally paid for it (since again you and the LLC are one and the same).
But you will have real costs.
You or the LLC may be able to deduct costs-of-sale, i.e. closing costs. There are very real costs in that real estate transaction. There may also be sales taxes amongst the various closing costs.
Also, this won't help you with tax assessments, as the assessor will simply ignore a below-market value and use market values. Worse, if your state has a Proposition 13 style law (which freezes tax assessment to value at the time of home purchase, so rising home values don't cause rising taxes and drive seniors etc. out of their lifetime homes)... the sale to the LLC will trigger a new tax assessment at market values.