My experience doing this for several large companies at a time is that the questionnaires don't really go away with certification. There are probably some shops where audit reports will substitute for the Excel spreadsheet Q&A's, but there are plenty of others where the Q&A is a dealbreaker part of procurements no matter what.
If you're in a line of business where your customers have questionnaires, just plan on having someone whose job is to fill these things out.
We got a SOC2... and still get questionnaires. It's the worst. Companies are just outsourcing their security reviews to the vendor. Rather than rely on a 3rd party audited document companies want their custom questions answered. BUT - they aren't custom questions - it's the same questions for every vendor and they are very often poorly worded. Then when we turn them in - there's no follow up questions which to me implies that no one is reading them. Security theater...
We have a SOC2 report type II, and security questionnaires/meetings are still there. Once we had a security questionnaire from a potential customer, took a glance at it, told the customer "hey you can find all of the answers in our SOC2 report and in our CAIQ (CSA)", they told us to still fill the questionnaire...
If you're in a line of business where your customers have questionnaires, just plan on having someone whose job is to fill these things out.