I think you're being over sensitive. It's 'because' we know she's going to die, whatever she's doing. Look at an episode of Casualty, where you get a dramatic build up to someone making a piece of toast and getting electrocuted. Toasters aren't dangerous per se, but you know because of the style of the show that this one will have a loose wire, or she'll spill her tea in it or something. Sometimes of course, they bluff you, and just when you're expecting the toaster electrocution, a gas main explodes.
If it had been 'Single Mother', then the minute the husband got on a motorbike, we'd have been going "oh, yes....."
I think if someone already has the idea that cycling is dangerous, the film will reinforce it. But so will every news story, or near miss they see. And their views are unlikely to be changed even if a character cycled the whole way through and never had a scratch.
At the very end, the other husband arrived with a bike, so it's clearly just seen as a way these people get around.