(The following assumes you have assets in your traditional IRA and Roth IRA that are greater than your perceived ready cash needs.)
It is probably not necessary to leave money in cash for quick access.
If you need quick access to cash, you can always sell your Roth investments and distribute the cash to yourself in a matter of a few days.
If the idea of doing that brings up the concern in your mind that you might have to "sell low" if the market is poor when you're in that pinch, then maybe you do want to have some cash. I don't think it's the best strategy, but if it helps you sleep at night then it's probably worth it for that reason.
A slightly more complicated middle ground is to keep your "in a pinch" cash in your traditional IRA. Then if you need cash quickly, sell from the Roth and distribute cash to yourself while simultaneously replacing the investments by buying in your traditional IRA with some of your "in a pinch" cash. Zero taxes this way, you maintain your AA, you have cash on hand, but the cash, while you wait, is in your traditional rather than your Roth.
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Personally, I have decided to have very minimal cash on hand, believing that the loss of investment return on the cash by keeping it uninvested during the majority of the time that I do not have a cash emergency outweighs the tax benefit of having ready cash in the few cases when I might need it. I've followed this policy for nine years now and have had zero big cash needs while remaining invested at 95%+ US equities, which have approximately doubled over that time frame.
Being partially pushed into the 24% bracket wouldn't really be that bad in my opinion. Because of RMDs and SS later and the associated higher brackets then, you might want to be voluntarily putting yourself in the 24% bracket now anyway (that is a larger discussion on Roth conversions).
Being pushed into the 32% bracket might be sort of bad, but I looked at the brackets just now and anything costing me that much is probably a bigger deal than the tax implications of it.
But my approach works for me because of my investing personality and my general lack of emergencies. If you're different in either of those respects, then my approach could easily be unappealing.