Q: I'm thinking of starting a new IRA. I know that traditional IRA contributions are deductible and Roth withdrawals are tax-free, but is this really worth losing access to my money until I'm 59 1/2?
IRA tax deductions are certainly valuable. In a traditional IRA like you mentioned, contributing the maximum of $6,000 in 2019 (assuming you're under 50) can get you a federal tax deduction worth $1,320 if you're in the 22% tax bracket. A similar value can be assigned to Roth withdrawals, but the benefit is obviously delayed.
Having said that, it's understandable that there's value in having ready access to your money in a standard (taxable) brokerage account. However, keep in mind that the traditional IRA deduction and tax-free Roth withdrawals are just some of the tax benefits of IRA investing. In fact, I wouldn't even call them the most valuable.
Specifically, money you invest in an IRA grows tax-deferred. This means that when a stock or fund you owns pays dividends, you don't have to pay dividend taxes, and if you sell an investment for a profit, you won't have to worry about capital gains tax. This can easily be worth tens of thousands of dollars over a few decades of IRA investing.
The tax benefits of IRAs and other retirement plans are extremely valuable, and aside from emergency savings, these accounts are almost always the best way to invest money for the long term. And you don't exactly "lose access." If you end up needing your money to cover unforeseen expenses, it'll just cost you a 10% early withdrawal penalty if you don't qualify for an exemption.