Why does FIPS 180-4 require the final padding block start with a 1?
If you don't start the padding with a $1$ it is not completely obvious where the padding starts.

If the message ends in

$...011010$

and you pad it to

$...01101000000$

which zeros were part of the message and which part of the padding?

If the padding is $1000...$ you know it started at the last $1$ in the padded string.

$...011010$

$...01101010000$

Edit:
Considering Why does the padding in Merkle–Damg&#229;rd hash functions like MD5 contain the message length?
This looks a bit like $10000...$ was used in the beginning and then the length was added for weaker assumptions on the compression function. In which case implementers probably complained that there are no real problems and that they didn't want to do any work, and that changes would require new certifications of products, etc. pp. and they ended up with this compromise which allows simply ignoring the last 64-bit block and using the old algorithms.