I think putting asset location in it's place within the investment decision process will help.
1. What is your goal? When will you need the money, and how much will you need? Included within this would be, which accounts are liquid?
2. What is your tolerance for risk?
3. Based on 1&2 decide your asset allocation.
4. Pick investments, which includes tax implications, so asset location goes here.
Now to your questions.
"1. If your tax-deferred account isn't liquid (putting aside a Roth conversion over 5 years, etc.), isn't it a bad idea to keep all equity in your taxable account?"
Yes, it would be a bad idea to keep the money you will need soon all in stocks. Within the decision tree, process #1 outranks process #4. The money you will need within 5 years(some would say 10 years) should probably be in bonds or cash. If you can't access your other accounts this means your taxable needs to be more conservative. When this isn't the case then you would put your most tax efficient investments, stock index ETFs, in the taxable account. So if you are still far from FIRE or you have access to other money, then you would use ETFs in the taxable, but if you need the money soon it makes sense to use bonds. If you need to use bonds in the taxable I would look into 'tax equivalent yields' to determine if you need taxable or muni bonds.
"2. Let's say you want to invest more in taxable bond funds for whatever reason. If you've already contributed the max to your tax-deferred account or otherwise are not eligible to deduct contributions to your tax-deferred account, wouldn't any further money invested to buy those bond funds be not deductible (and therefore defeating one of the main benefits of contributing to a tax-deferred account)? "
In case this part wasn't known, you can always exchange investments within an IRA or 401k with no tax implications*. So if you have stocks in the 401k you can switch them to bonds. If your pre-tax accounts are already 100% bonds and you need to add more bonds then you should add bonds to the taxable account. In this case, process #3 is overriding process #4.
Example: 700k in taxable, all stock ETFs. 300k in 401k, all bonds. You are currently 70% stocks and 30% bonds. What if you want to get to 60/40. Well you would need to hold 100k worth of bonds in the taxable account. Your goals, tolerance for risk, and AA are more important that tax efficiency.
*Exception being if you are adding an investment that can't go into an IRA, like your own home. This is very rare.