These are my guesses. Not sure how educated they are.
I'd expect it to depend on the nature of the post-Brexit relationship between the UK and the EU. They will have some sort of treaty or agreement on trade, and that will probably include something about handling taxes.
In the best case they cooperate fully and keep the VAT MOSS system working like it does now. That will result in no change from a VAT reporting and collection point of view.
In the worst case they do not cooperate. The consequences of that depend on where the seller is located.
If the seller is not in the UK and not in the EU, then the result is to approximately double the quarterly paperwork. Instead of reporting to the VAT MOSS system of one country and having it distribute the tax to all the others, they will have to report to one EU country VAT MOSS to deal with all of the EU, and to the UK tax authorities to deal with VAT for UK customers. My guess is that those currently using UK VAT MOSS will most likely switch to Ireland VAT MOSS for their EU VAT, to stick with an English speaking country.
If the seller is in the UK, and not in the EU, then the "do not cooperate" case is not as big an impact. That's because the UK VAT MOSS system cannot be used by UK merchants to report UK VAT. They can only use it to report non-UK VAT. They have to file separate paperwork with the UK tax authorities for UK VAT. So worst case for these sellers is that UK VAT MOSS goes away and they have to register with some EU country's VAT MOSS to deal with EU VAT. After that, they are essentially in the same position they are now: they are still reporting to both the UK tax authority and to a VAT MOSS. All that changes is that they might have to use a different VAT MOSS.
My guess would be that it is because each country has its own rules about how VAT works for for things sold to buyers in their country. Each country would like to fully apply its rules to all purchases by its residents, but they recognize that it would be unwieldy and expensive for sellers to have to deal with minutia of the VAT rules of a couple dozen different countries.
VAT MOSS is a compromise that simplifies the rules, so that a seller selling into several foreign EU countries only has to deal with one unified set of rules through the VAT system. Instead of having to know details of the tax law of several countries, the seller only need to know the VAT rate for each. That's much easier to deal with.
I'd guess that they don't apply VAT MOSS to sales by domestic sellers to domestic buyers because they consider their own tax rules superior to the rules under VAT MOSS.
I'd expect it to depend on the nature of the post-Brexit relationship between the UK and the EU. They will have some sort of treaty or agreement on trade, and that will probably include something about handling taxes.
In the best case they cooperate fully and keep the VAT MOSS system working like it does now. That will result in no change from a VAT reporting and collection point of view.
In the worst case they do not cooperate. The consequences of that depend on where the seller is located.
If the seller is not in the UK and not in the EU, then the result is to approximately double the quarterly paperwork. Instead of reporting to the VAT MOSS system of one country and having it distribute the tax to all the others, they will have to report to one EU country VAT MOSS to deal with all of the EU, and to the UK tax authorities to deal with VAT for UK customers. My guess is that those currently using UK VAT MOSS will most likely switch to Ireland VAT MOSS for their EU VAT, to stick with an English speaking country.
If the seller is in the UK, and not in the EU, then the "do not cooperate" case is not as big an impact. That's because the UK VAT MOSS system cannot be used by UK merchants to report UK VAT. They can only use it to report non-UK VAT. They have to file separate paperwork with the UK tax authorities for UK VAT. So worst case for these sellers is that UK VAT MOSS goes away and they have to register with some EU country's VAT MOSS to deal with EU VAT. After that, they are essentially in the same position they are now: they are still reporting to both the UK tax authority and to a VAT MOSS. All that changes is that they might have to use a different VAT MOSS.