What I find odd is that there are no DME/ALT checks after 1600' at 4.8nm. EFIS a/c do LNAV/VNAV descents to MDA. (the chart shown in #17 is not an RNAV approach. Is there one?) However, older, perhaps more private a/c are steam driven. This would invite, especially over the obstacle free sea, a Dive & Drive profile. Either way, the crew procedures should be a level off at 500' or 770' until 2nm and a decision if the runway is in sight yes/no. Then a land or GA decision.
I have to admit, if was in my (dream on) private twin prop on a murky day with a hot date waiting, I might be tempted to shave a bit off (if you get my drift) and nibble below the belt to see if I could get in. However, I would not like a crowd to join me, so I think in a B738 case I'd be respecting my master and his rules.