I can't speak for all services but this certainly isn't the case in any of the NHS mh services I've worked in or been involved in.
Expressing suicidal ideation/attempting suicide is a risk factor for a future successful attempt.
However the role of a secondary care MH team/crisis team is to try and support the person to link up with the right treatment/support that's going to have a positive impact on their overall mood and wellbeing, with the idea that improving their mood will reduce suicidal ideation.
There aren't the resources to offer a bed in a ward to everyone that expresses suicidal ideation or attempts suicide, unfortunately. It's far more common than many people realise.
And the difficult truth is that even with the right support and treatment, there will always be people that end up taking their own lives. It has been the case throughout all of humankind. You can't lock someone in a padded room 24/7 forever, people have agency and rights to live their life and we rightly have a high bar for removing someone's liberty. You can't prevent it directly, what you can do is properly fund and staff services so that people with mental health difficulties get the right treatment at the right time. Suicidal ideation is often a symptom of a disorder/circumstances rather than the primary problem.
Secondary care crisis services aren't equipped to offer the actual treatment people need, other than arranging for medication. So they direct patients to the right place.
The person in your OP is clearly in crisis and I hope they get the right support.