Anne & I were talking about these over dinner. While $300k is a lot for 10 bike shelters, and the money could have easily gone toward just installing a ton more individual U-shaped racks all around the city, I do think there is some value in showcasing these types of eye-catching showpieces that not only serve a specific function, they declare to the world that "this is something of importance here".
It's an indirect benefit, but this can cause a change in culture, and an eventual mindset shift both for cyclists and motorists.
Additionally, I've seen countless examples of discussions started around here (and elsewhere) with a photo of something (like a bike shelter) in another city and a proclamation of "Why can't Columbus have something like this?". Rarely is cost brought up in those conversations. And I imagine that there are complaints about costs in other cities too, but we're a step removed from all of that.
Anyway, yeah, public infrastructure installation is expensive. All kinds.
I don't know if it's the cost as much as it is the question of the benefit relative to that cost. Warm, fuzzy feelings of inclusion and awareness are awesome but from a practical stand point what do they do for me if I ride my bike?
Something as simple as a bike pump coupled with some graphic illustrations (done, of course, in partnership with the deep and rich pool of artists and designers) instructing one on how to change a flat would benefit cyclists in a much more practical and tangible way.
Incorporating a bike counter of some sort to measure usage, ridership patterns and so on would benefit the city immensely when it comes to further improvements and enhancements.
I love this city and what it's doing to promote alternatives. Ultimately that goes a long way to promote the culture shift you speak of. Unfortunately there is a lack of innovation and a lack of openness to new ideas or dissent. If this city wants to be a world class bike city, it needs to move away from bike shacks and prefacing it's work with "it works in ____".