Input credit on input services not available to claim in switchover from composition to regular

This is because you have already consumed the service as and when it was provided. Since you consumed it during composition scheme therefore ITC will not be available. And for this reason also there is no stock of services being intangible and consumed as and when provided. Therefore transfer of ITC of services is not possible.

How can that be the case, as long as we have unsold stock, tax paid on services availed with respect to its production still remain. For instance, if there is a business which produces product 'x' and sells it. for making the product, it hires services of a professional (say designer) and as a result pays him his fees which includes gst. now this gst paid on input service if not available for credit, then wouldn't there be double taxation as now the fees of professional is part of production cost of product 'x' and when selling it further not just that professional fees paid is to be recovered but also gst paid on it, as it's credit is not available even the gst paid on it will be added to its cost.
This is my doubt.