Hmmmm.. I do not know why there is a checkbox for Show Price.. that is not normally in the WooCommerce product form.
SO when your vendors add a product from their pro dashboard front-end form, and then submit, the product is live but it does not have an add to cart button?
DO you have these capabilities enabled: (wp admin > woocommerce > wc vendors > capabilities– you ALLOW Submit products and Submit products live without requiring approval)
If you switch to the Storefront theme (temporarily) and disable all plugins except WooCommerce, WC Vendors and WC Vendors Pro, then go to add a product as a vendor, does this still happen?
If not, re-activate your theme– then test.
If it is still working properly, re-activate your plugins one by one until you find the one that is causing this issue.