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Why? If the UK leaves the EU without an agreement (Hard Brexit), UK national are regarded as any national outside of the EU. The only advantage UK national will have is that they do not need a visa to enter the EU (see excerpt from ETIAS site).
https://www.etiasvisa.com/etias-news/etias-visa-how-will-it-affect-uk-citizens

Quote:
The EU Commission has confirmed that UK citizens will need to pay a fee to visit Europe after Brexit. From 2021, when British citizens travel to Europe they will need to complete the online ETIAS application formbefore setting off.

UK citizens will not need to apply for a Schengen Visa like many other nationalities. On February 1, 2019, the European Council said: “EU ambassadors today agreed that, following Brexit, UK citizens coming to the Schengen area for a short stay (90 days in any 180 days) should be granted visa-free travel.”
Even though there are many things that are still uncertain for Britain, one thing British citizens won't have to worry about is applying for a visa to visit EU member countries. On April 4th, the European Parliament passed a law in Brussels by 502 votes to 81. The law establishes that Britons can travel to Europe visa-free. Euro-MPs ruled that anyone with British citizenship traveling to mainland Europe for stays under 90 days is not expected to get a visa.
However, implementation of the law is conditioned. Members of parliament also said this is conditional upon the UK granting EU nationals the same benefits. This means British travelers will only be visa-exempt as long as EU citizens can enter the UK without a visa.
British travelers will still need to apply for ETIAS. ETIAS (European Travel Information and Authorisation System) is the name given to the new travel authorization system which will be a requirement for British citizens and 60 other nationalities who can currently visit Europe visa-free.
While the UK is still a member of the EU, UK citizens traveling to Europe only need their passport to enter the other member countries. However, this will change after Brexit and, from 2021, ETIAS for British citizens will be a requirement.
The ETIAS visa waiver for Europe is being developed to improve the security and border control of Europe following concerns over terrorism and immigration. It will be similar to both the US (ESTA) and Canadian (eTA) models which have already been implemented.
When people apply for ETIAS, they will be screened using a number of European security databases including Interpol and Europol. Anyone who poses a security threat will be identified and prevented from reaching European soil.