Question: why not use my machine to sew something like a dot of satin stitch or some other dense stitch to "tie" a quilt. Wouldn't this be easier? Also safer for kids?

I think someone posted a pic of a quilt kinda like that yesterday. There were small blocks with satin stitching around them throughout the quilt. She told me they were the "ties". It was really really pretty!

Don't know why it wouldn't work,

Keep in mind part of the reason for tying is the dificulty of handling all the fabric in the machine, and keeping the top and bottom stretched at the same time, for a consistant top and botton, can get pulled one way or the other going under the foot, then it may lay funny.
Have to ask, how are kids going to get hurt with a tye?

I wondered too.

As long as you still baste it in some way first I think it is a wonderful idea :D:D:D

Sounds workable....maybe do a practice patch first. Can't quite see how a tied quilt could be harmful to a child, the only thing I wouldn't use on a small person's quilt is monofilament.

I've done it. Works great.

If you don't tie the tie down well enough, it could come loose and become a choking hazard. 'Course, same could be said of loose threads.

I'm a nanny and have one client who won't even give her toddler stuffed animals with buttons, 'cause if they come loose, he could choke. Personally, I think that's worrying too much.

Machine "tying" works well. I have done it on several because I worried about the chocking hazard.

If you tie a quilt and tie the ties TIGHTLY three times they won't come untied. Also trim the strings down to about 1/2 to 3/4 of an inch and they aren't long enough to get choked on. Quilts have been being tied for hundreds of years with no problems. However, you can machine tie if you want, it's just another form of quilting.