There is always a need to compete, putting up protectionist barriers doesn't remove the need, it just delays the day of reckoning whilst forcing consumers to put up with monopolistic shitehocs like the Royal Mail, who treat their workers like shit and their customers like shit.
Sorry, some more thoughts:
It's not just competing with other businesses, it's that other businesses have had time to become entrenched in other regions. Most of ours that are already entrenched in the EU and UK with corporate brand recognition, for them if they have to pull out of that entrenchment then there are risks they won't be able to even break into the other markets because of that entrenchment. So if they can't keep their current levels of Europe-focused business and growth post-Brexit, that's a problem for them.
There's also the issue that for middleman businesses (aka services), European businesses can work on different payment models compared to other parts of the world. For example, where I get work we get paid on commission in Europe but rest of the world often operates on upfront payments for the service with less commission. So businesses where that applies may have adjust their business models, with all the overhead of setting that new technical infrastructure up, financial infrastructure, and building the different skill sets. Again, if they need to reduce involvement in the EU this is going to cause issues that could damage our current businesses.
Also if you're a part of a large global organisation, they often already have their America and China branches. Sometimes even a Middle East branch. For those businesses, the offices they set up are valued for regional skill-set and proximity to customers. So if you have a UK office that can only reach places the UK and then a bunch in much different time zones and speaking different languages, but no longer has the same reach into our immediate neighbouring countries, you're going to have a UK office just for the UK, a Europe office for the EU in the EU (probably in Berlin), and an American office for USA/Canada, and a China office for China. Which is the risk of reduced 'foreign investment' slowing growth.
So when you put someone in charge of Leaving that isn't a fanatic who wants to Leave no matter the costs, suddenly the self-preservation instinct that the political party in charge is going to take the bulk of the blame from the people who work for those businesses now will kick in. So they have to find a leaving agreement that doesn't result in that harm. And if they're a fanatic, they put their fingers in their ears the whole time and the damage gets done because that's what fanatics do. And the rest of their party suddenly have their self-preservation instincts kick in and work to not allow that to happen.
Hence, the current inevitable clusterfuck.