The video below warns us about "the sinners prayer". And there is indeed a problem with the preaching of many evangelists. But let's locate the problem where it belongs.
The problem with offering salvation freely is not the freeness of the offer, it's the definition of salvation. If salvation is stuff - forgiveness of sins, cleansing from guilt, eternal fire insurance, "life to the full" - then offering it freely is like telling your mates they can borrow your next-door neighbour's lawn-mower. Just because you can use it freely doesn't mean everyone else can. You can use it freely because you're in relationship with your neighbour.
Now if your neighbour was very generous, he might lend it out to all who come to his front-door and ask. But you don't honour his generosity by giving it away impersonally.
There is a deeper problem than easy believism. The deeper problem is offering gospel commodities. And that problem is not alleviated by selling them on at a high price! That only compounds the problem.
Imagine that I undertook to sell-on the use of my neighbour's lawnmower at a handsome hourly rate, because I wanted to honour the costliness of my neighbour's gift. Of course I might not be honouring my neighbour at all if I broker such deals. Because - what if the deepest joy of my neighbour was not lending out his stuff, but getting to know his neighbours personally? And what if my "handsome hourly rate" only ends up advertising how tightfisted he is around the neighbourhood??
There is nothing wrong with a free gospel offer. So long as what we are offering is not a what, but a Who. Don't offer stuff for free. And don't offer stuff for a price. Offer them Christ. And offer Him for free, because that is what most honours His free self-offering.