They have something like that on the platform at Ipswich station, with access to whomsoever joined the queue first back whenever they set it up. I didn't join said queue as I don't get trains that often - I reckoned it was best left for daily commuters. No idea if a charge is involved, there is a secret code to access.
I suggested about a year ago that they audit the users as it seemed rather empty.
The rest of us have to take our luck outside the station, approx the other side of the fence that's next to this cage, accessible to all comers. tbh I don't think moving to the station multistorey would help any, and may make more people with handy bike-carrying-away devices aware of its existence. It's certainly an improvement on the previous location - it's properly sheltered (think platform canopy) and less obvious and more overlooked.