As the parent of a kid who doesn't have any close friends, I feel for LW, but yeah, you can't force a friendship. People over the age of about 4 either like spending time together or they don't; you're not going to change their mind by forcing them to play together, and indeed you might be setting your kid up for being bullied.

If four years from now LW was called by a parent who said "Your daughter doesn't want to date my son; we need to fix that", would LW go "sure" or "no flipping way; my daughter gets to decide who she wants to be in a relationship with"? Friendship works like romantic and sexual relationships; both parties have to be interested for it to work.