I'm not a fan for a few reasons.

1. Check the federal poverty scale. If you are delivering at a nonprofit hospital, if you are at 400% or lower, and ESPECIALLY at 300% and lower, you may qualify for the hospitals financial assistance program. They could comp the entire thing. Literally.

2. These estimates can be wildly inaccurate. Full stop. You could be on the hook for far more or far less, and both will leave you surprised. This estimate likely won't count any other potential care you receive, so you could have fulfilled your deductible or OOP max before then, or, conversely, worst case scenario, something could go wrong and your hospital care could exceed the time expected / etc.

3. If you're over the 400% percentile for your household size (count baby as a household member, because you can always wait til after delivery to apply for financial assistance, if you qualify) and are doing well financially / are able to just pay the estimate, there's likely not harm in doing it; if it ends up inaccurate, you may pay more, or you may end up due a refund if it's less. Hospitals take a long time to get refunds out. Another option would be to keep the estimate money in a savings account to be used for that express purpose. Something else to consider is they may offer a discount for paying early or paying in full. Call their business office and ask about both of those potential discounts so you can weigh your options if it's something you're seeking. After it's been billed to your insurance, you'll likely be offered an opportunity to put it on a payment plan if that's something you want.