Can I optimized HD by using a time machine restore?

No and NO.. and really don't do it.

You will get no improvement whatsoever.

The old stuff about optimising disks is all finished.. If the disk is slow in your Mac replace it with SSD.

Is this new total Time Machine backup in some way 'optimized' -- maybe the data better organized on the disk?

The Time Machine data is simply a copy of the data your Mac. Nothing more....nothing less.

if I was to now erase my HD and restore from this new Time Machine fresh backup, would that be good?

There would be absolutely no benefit at all to doing this. All that you are doing is copying the same data from one drive to another.

Or have I started believing some unfounded computer myths and urban legends?

We have no idea what you might have "heard" from another source. But, if they are claiming to "optimize", "clean", "keep", "speed up", or anything like this.......they are a scam.

If your disk has bad sectors that require a reformat, then erasing and restoring from a Time Machine backup would be good idea. Otherwise, you'll be wasting your time.