> For example, if you sold your house for $2m, your effective tax rate on the sale would be 5%
The tax on capital gains in this case would be 20% federal, ~10% state (in California), 3.8% ACA investment tax. That's an ~34% rate, not the 20% you seem to think applies.
> the only cash you need to come up with is the down payment for the new house
Let's take the simple case where the old house was paid off, no mortgage. Are you suggesting that it's unreasonable to want to downsize and still not have a mortgage?
If you do have a significant mortgage, and are hence highly leveraged, an increase in property prices is pretty good. If your mortgage is more or less paid off, you can in fact end up in a situation where you can't buy any house at all in the same general market after selling your existing one and paying the property taxes. See a worked-out example at https://news.ycombinator.com/item?id=15706565