//So in reality, the EU’s free movement of people allows free movement to any member State for up to three months, and to work in any member State//
Absolute hogwash.
I'm well aware of the passage you quoted. You should be aware that whenever I've mentioned that right, I've always referred to it as the right to "work and settle" here. But that is of little importance.
In practice, whilst we were EU members, the UK had no right to deny entry to EU citizens. They could not be questioned at the border (even if the resources to do so were available) and all had the unfettered right of entry (bar one or two very exceptional circumstances where those convicted of serious criminal offences were concerned).
Once here, there was no way on Earth that the UK authorities could check whether or not they had complied with the conditions you quote. Do you think it was practical for the Immigration people to pop round to every one of them and ask them if they've managed to get a job? Bear in mind that when the permanent settlement scheme for EU citizens was set up post Brexit, some 5.5m applied for residency. Do you think the resources are available to check on that number of people? If any were found to be staying contrary to the rights you have quoted, do you think the UK would deport them promptly? If you're going to debate these matters you need to separate theory from practice (i.e. get real).
// – but they cannot become a burden on another host country..//
I've never mentioned anything about them becoming a burden. That isn't the issue (see below).
//Who could possibly object to such a sensible arrangement, allowing such freedoms to their citizens?//
Anybody who bothers to ponder how accommodation and public services are to be provided for such a large influx. This country is desperately short of housing and its public services - healthcare and education in particular - are creaking at the seams. There is nothing sensible about allowing such an arrangement.
//So there is no way that many millions of EU citizens could just roll up in the UK, as claimed by the xenophobic/racist Brexiteers.//
As above, there most certainly is. And I would thank you not to label people - in particular me - who voted to leave as racist or xenophobic. I am neither, but I do think things through, whilst it is quite evident that you do not.