Do you think that the majority of Eastern Europeans that came here came because of benefits or due to the fact the wages and potential standard of living is higher. If the former I am sure you are wrong, if the later this is the reason why you would have a flood of people coming to the UK until the differential between their country and ours is diminished (either theirs goes up or more likely ours go down). There are currently 100's of millions of people where this is the case and there is no safety net in their own country. They wont have to walk here as they can jump on a boat or plane as we will be allowing anyone to enter - not everyone would be able to afford the cost but a lot would, they may prefer to go to a country with more protection but they wont let them in.
Once here they may wish to go to another country with access to benefits but this would not be open to them without engaging people smugglers, only a small percentage would be willing / able to go down that route. There would be little to no incentive to go to another country other than the UK as it would be likely that the only other countries to allow access would be those with a lower standard of living.
Result would be 10's millions extra people on the Island, lower wages and very likely social unrest.
Sometimes you become entrenched in the "market knows best", its almost a religion.