Time on an LOC approach in a medium/heavy jet is in most case completely irrelevant as a normal approach to the touchdown zone using normal maneuvers would be impossible. Better techniques involve calculating your own VDP. I would hope you start your climb before reaching the actual MAP.

In the United States, if you are clear for the ILS you are also clear to fly the LOC approach. The reason it might be confusing to some pilots is because ATC has to use the actual title of the approach plate to clear you for a particular approach. If the approach is titled ILS 12 and you want to fly the LOC 12, ATC will have to clear you for the ILS 12 approach. If the glideslope is inop, ATC still has to clear you for the ILS 12 approach but should include the comment "glideslope inop" (while not mandatory).

This made is particularly confusing to international flight crews. If you fly in Europe and you want to fly the LOC approach you will look for the LOC approach plate and not the ILS. FAA is slowly meeting ICAO standards naming more and more approach "ILS or LOC" to prevent in part this little confusion and for ATC to clear you for the correct approach.