Placement of fuse on neutral wire. Why?
So, my question is, am I missing something?

Yup.
You're correct: a blown fuse on the neutral means the circuit is still live rather than a blown fuse on the hot where the circuit would be dead. It is always better to fuse the line side.
Q: How do you tell which side is hot?
A: We can't.
Graphs and schematics are nice but the piece of the puzzle you're missing lies with J2. A simple power connector, part number 770W-X2/10, is an IEC 320-C8, Non-Polarized receptacle. It doesn't matter which side the fuse is one, they're both quasi-line-side. If the connector were plugged in such that the top was 'L' and the bottom was 'N', great. However, it's equally likely that it is flipped and the top is 'N' and the bottom is 'L'. There's no real benefit to be gained here since we don't know.
As for why the designer didn't just draw the fuse on 'L' -- I don't know. Maybe to make you question your knowledge on fuses.

Or are those who designed these circuits just missing an opportunity to make their circuits possibly safer [...]?

Using a polarized connector they could guarantee the line side is fused. For clarification, this would also require that the plug is polarized as well. Not all countries use polarized plugs. Although it is &quot;Texas&quot; Instruments, they design and sell globally.

I guess a bigger point here is that we're misunderstanding the circuit as a whole. What exactly is this circuit for? It's a 50/100W Audio Power Supply but if we pull it up on TI we can see that this circuit is part of a product that is for &quot;testing and performance validation only, not available for sale&quot;. The PDF further labels it as a reference design. So, we do need to take TI's disclaimer into account here:

These resources are intended for skilled developers designing with TI products. You are solely responsible for (1) selecting the appropriate
TI products for your application, (2) designing, validating and testing your application, and (3) ensuring your application meets applicable
standards, and any other safety, security, or other requirements.

It is not TI's intention that you go plugging this in around the world amazed that it works everywhere, rather, you decide that it is going to work with 120 V in North America, and you would adjust J2 to be something like an IEC C14. If you were to use this circuit at 220 V in Europe and design it around a CEE7/16 Europlug, you'd want to add another fuse since that's basically two hots.