Re: Why anyway ?
Minor nitpick, Freedom of Movement has nothing to do with border control. The people at the border don't care about your FoM status, it's not their job, will never be their job and it couldn't even be their job.
Freedom of Movement is not about the right to pass a border, it is about the right to live, work and own property in another country. There are countries in Europe that have no border controls but also no Freedom of Movement (Liechtenstein for instance). There are countries in Europe with Freedom of movement and border control (Ireland and the UK for instance).
The people at the border check for someone's eligibility to enter the country, not their eligibility to work there. They couldn't because it is impossible for someone at a border booth to tell if someone is coming to the country to work or for a ten day vacation. If they have a valid visa or are from a country with a visa waiver they can come in. Some people might overstay their visa or work on a tourist visa but there is no way to positively predict that when someone arrives at the border.
Ultimately immigration is not a border issue, it is something that is dealt with behind the border, when applying for a National Insurance Number for instance. Or requiring employers to make sure their staff are eligible to work in the country. To a limited degree it is also dealt with before the border, when someone from a 'risky' country applies for a visa for a holiday but doesn't have the funds to pay for a three week trek through the country, can't show proof of hotel bookings or return flights etc.
Don't expect the UK Government to understand this though, they wouldn't be where they are now if they knew what they were doing. Theresa May has been Home Secretary for six years and still doesn't understand the difference between immigration and border control.