It honestly depends on the time of year you are going. During higher occupancy, more total rooms are occupied. So that means less of a selection. So arriving later in the day, can mean less of a choice. Now, some reservations are for different room types and guaranteed. In that case, the room is blocked for you so that other guess could have left at 6am and the room is just waiting.
What happen in hotels is the rooms are blocked a few days to a week out for the upcoming arrivals for that day. Paid upgraded rooms are matched first (ie you paid for a suite or bunk bed room, you are matched up with a departure from that day). However run of the house inventory rooms are blocked normally on location. This is due to housekeeping and making the turning of rooms more labor efficient. So if you have say 250 general rooms leaving that day with 260 arrivals (yes all hotels overbook on purpose), and you come in late in the day, you might be stuck with the least disa desirable room.