Saving More for Retirement - Trad IRA vs Normal Brokerage Account

I'm trying to understand what would someone's logic be for opening a Traditional IRA versus just using a plain ole brokerage account for long term investing + saving for retirement in my situation. I'll preface with some pertinent information:

- Primary income is from W2 / salaried employee
- 401K through my company that I max out
- I have a Roth IRA but I make too much money (W2) to contribute going forward; AKA I'm over the contribution threshold
- I have a normal brokerage account with a modest amount of money ($50K) that I 'play' with (ex. usually these are L/T investments in individual companies I target, but sometimes I use it to take fliers (SLI))
- HYS account with about 4-5 months of living expenses
- Due to a long term and very expensive medication I am on, the HSA route will not work in my situation

So, if I want to save more for retirement over the top of my 401K and Roth IRA, what is the advantage for opening a personal / Traditional IRA versus just using my brokerage account for that? With a Traditional IRA, I'm still contributing after tax dollars, right? And then I'll get taxed again when I withdraw, whether it be voluntary or mandatory.

I understand some may say that Trad IRA contributions can be tax deductible. But since I have an employer-sponsored retirement plan, the tax-deductible portion of my IRA contribution is most likely going to be limited.

Any help is greatly appreciated!

TL/DR - what is the advantage for contributing to a Trad IRA instead of just using a normal brokerage account in order to save more for retirement.