Platforms such as Google normally don't allow deleting profiles. See how to act when business is closing or doesn't exist anymore.
Platforms such as Google don't normally allow deleting profiles from the platform. Therefore, Localistico cannot do that either unless the platforms decide to change their policy. The reason behind this way of working is that platforms think that it is misleading for the customers if the profile just disappears from Google Maps, for example. The correct way of closing down a business on Google is to mark is as permanently closed. This is how you can do it from Localistico. This way, the customer knows that the location is no longer receiving customers and will search for the next closest location.
Be careful with Google My Business Profile, in the platform they display a button "remove business". This doesn't delete the business, it only removes it from your account, but the profile keeps appearing in searches for the users, and they can leave reviews or edit the information of those profiles.
When a business has been marked as permanently closed on Google, it will get removed eventually by the platform itself. Please note that Google, for example, doesn't give you any timeline on how long this will take, and it can take even one year or more.