Does the trapped capital actually matter if the property cash flows?

You're describing it correctly. 22k left in a property worth 185k with a 138k loan is a rental bought at a discount with a 12% down payment equivalent, and if it covers debt service it's a fine asset. The word "trapped" carries a judgment that the numbers don't always support.

Where it turns into a real cost is in three places your model probably isn't showing. First, the shortfall usually doesn't arrive alone. An appraisal 20k light often means the rehab also ran over or the rent comps came in soft, and those correlate because they're all reading the same submarket. Model the 185k appraisal with rent 8% below your projection and see whether coverage still holds.

Second, your reserve position. If the 22k came out of the same pot you were holding as reserves, you now own a rental with no cushion, and the first 6k HVAC failure puts you on a credit card. Operators who blow up rarely blow up on the deal math, they blow up on having nothing liquid when two things break at once.

Third, the compounding. One deal a year instead of two isn't a 50% reduction in pace, it's a difference that widens every year, and the capital you're not recycling is capital not earning the acquisition discount that makes this strategy work at all. That's the reason the reputation is harsh.

The assumption I'd stress is your 75% LTV. Cash-out refinance LTVs on non-owner-occupied property differ by lender and by product, and some come in lower than 75% on a two-to-four unit. Confirm the actual number in writing with your lender for your specific property type before you underwrite off it, because the whole thing swings on that one figure.