Any nation state has a range of options in how it trades with other nation states. The choice is completely free but each choice comes with consequences. Making a particular choice but expecting not to endure the consequences is madness:
1 You can opt to be a closed country and not trade at all with any other country. Japan did this for a few hundred years. You have total sovereignty. You can have whatever rules and regulations that you want. Nobody can impose any rules at all on you.
2 You can trade with another nation under strict controls. You can impose quotas and tariffs. Either you agree quotas and tariffs with the other nation or you impose them unilaterally and suffer whatever the other nation does in response. You still have complete control over your rules and regulations although companies in your country will have to obey the rules and regulations of the other country in order to export to them. All trade has to undergo some form of customs checks to ensure that they conform to the rules and regulations of the country they are going to, that they are within the quotas and that all tariffs have been paid.
3 You can apply to become a member of the WTO and, if you are accepted, you will need to obey all WTO rules. You can largely have control over your rules and regulations but only within the scope of what WTO rules allow. You can have quotas and tariffs but they also need to be within WTO rules. The advantage of being a member is that you have somewhere to complain if you are treated unfairly by another country. The price you pay is that you don't have complete control over your rules and regulations. All trade still has to undergo some form of customs checks to ensure that they conform to the rules and regulations of the country they are going to, that they are within the quotas and that all tariffs have been paid..
4 You can enter into a Free Trade Agreement with another country. Under that both countries agree to abolish quotas and tariffs. Exactly how you do that is a matter between the two countries, although WTO rules put some limitations on what is allowed. Many people don't seem to realise that having different rules and regulations in the two countries in itself acts as a barrier to free trade and so countries usually want to check that their rules and regulations are equivalent. They don't need to be in total alignment but there does have to be broad equivalence otherwise one country might have a competitive advantage over the other. It is this aspect of negotiating a free trade deal that takes the longest and it may involves both countries amending their rules and regulations to some extent. Yet more loss of total sovereignty to gain better trade. Because the rules and regulations are not completely aligned all trade still has to undergo some form of customs checks to ensure that they conform to the rules and regulations of the country they are going to.
5 You can enter into a customs union with another country. In this case you not only agree to no quotas and no tariffs but also to complete alignment of your rules and regulations. Because the rules and regulations are aligned you do not need any customs checks on the movement of goods. This gives by far the best trading arrangement but also involves the biggest loss of sovereignty for both countries.
Notice that option 1 does not require customs checks because there is no trade to check. Options 2, 3 and 4 all require customs checks. Option 5 does not require customs checks because of regulatory alignment. The above options apply to all world trade. All trade is carried out under one of these options. Brexit from day one has made two completely incompatible demands. The UK wants to move from option 5, where it is now, to either option 4 or option 3 BUT it does not want customs checks between Northern Ireland and the Republic, because of the Belfast (Good Friday) Agreement. It claims it can resolve this dichotomy by technological means but there is no convincing evidence that the technology exists or how quickly it can be implemented. I am sure such solutions can be implemented but I do not know how long they would take. It is not surprising, therefore, that the EU want a backstop in which at least Northern Ireland stays in the customs union until such times as the FTA has been finalised and the technological; solutions implemented. It's also totally logical that the backstop, if implemented would have to exist until technological solutions had been implemented to the satisfaction of both the EU and the UK. Hence it cannot be time limited or unilaterally abandoned.
I am sure the EU would prefer the UK to stay in the EU. I am sure the EU does not want other EU states to follow the UK down the exit road. While I am sure these assertions are true I do not believe that the whole EU negotiation is based around these ideas. The negotiation is based around the the basic principles of trade outlined in options 1 to 5 above. Every aspect of it follows the logic of of those options. Trade deals with other countries fit within these options. Norway, for example, is within EEA, so it follows the freedoms required for members of the single market but it is not in the customs union so it undergoes customs checks. Switzerland is not technically within the EEA, but it bilaterally sticks close to its rules, and is not in the customs union and so it also undergoes customs checks. The EU have been highly flexible in what they have offered. The UK could have Norway Plus and stay in both the single market and the customs union. It could have Norway, i.e. in the single market but not the customs union. It could have a Canada style FTA. It could have Canada Plus, i.e. a Canada style FTA but wider reaching. All these fit within the 5 options. All have consequences. Parliament will not agree to any of them.
My mother used to tell a story of when I was 4 years old. Apparently we were out shopping and met a close friend of the family who stopped to chat. As he was leaving he gave me a sixpence, which I put in my pocket. A short time later we were in Woolworths and I saw a small bell that I fancied and which happened to cost sixpence. I asked my mother if I could have the bell and she said, "Of course you can. You can buy it with the sixpence you were given". I thought for a short while, picked up the bell, rang it a few times and put it back on the counter. I went home with the sixpence still in my pocket. I learnt at 4 years old that you can't have both the bell and the sixpence. Some people, many of them in parliament today, never learn this lesson in life.