That's pretty much what I do. Let them fight it if they do. Dot did one time, and did fall down. I think it was more out of a temper tantrum, like you said.
Why would cross ties be safer?
I have a tree that I have a lead rope tied to that keeps their head at the level cross ties would. Long enough for them to be comfortable, but not long enough to get a leg hung up in.
Becky
The one plus the cross ties have is the footing is less secure for them in that they are on concrete, not dirt.
I don't think they actually learn to stand tied until they fight it and can't get loose.
I think they are safer cross tied than tying to something like a trailer or a bar they would get under if they pulled back on. The ground around and under them can be completely clear. Your tree is good. They can't hurt themselves on it and they aren't going to pull that over. But anything man-made, including posts, wall, tie rings on trailers or snaps on lead ropes, if they want to break it they can, especially if they can get really good footing.
I think we tied ours fairly young - measured in months... before she had the strength to break anything... but I didn't leave them unattended and would untie the knot but keep hold of the lead through the ring if they started pulling, untill I could settle them down again.