It's to increase occupancy and profit and they will probably claim it's so they can afford to offer the best prices to customers.
From experience they will know that X% of people don't turn up, so if the hotel has 100 rooms, they know that they can book, say up to 102 rooms and nearly always have at least 2 people not show up, so not a problem.
Hotels have all sorts of complicated algorithms based on average occupancy, probably events in the area, time of year, in the week or at weekends and probably other stuff as well.
They say that the problem that the OP has had where there wasn't room for her only affects 0.2% of cases, so it's only 1 in 500 people that they have to reaccomodate at other Travelodges.
And in most cases they will be able to but in this case, they haven't been able to give a room to the OP but the worst thing is that they've gone against their own policy of not bumping single female travellers, but in reality, they shouldn't leave anyone without a room and if there isn't an alternative nearby or the customer doesn't accept it (I wouldn't really want to drive to the other side of Manchester in the middle of the night, and I am reasonably familiar with the area. If I had felt capable of driving, I might have accepted it if they were willing to give me the room for free, or a significant discount for the inconvenience) then they should book them into any other nearby hotel, even if it costs them money, because they've made extra money in the past on their no show policy many times more than thist when rooms have been paid for twice and they haven't been caught out.