I don't really agree here. I think what they are doing is pretty strategic, especially given the relatively limited money they have.
There's basically two sides to funding software that are actually rather different
1. Accelerator phase: getting the software to a point where it can reasonably replace some foreign closed source enterprise option (i.e. feature devlopment). This sort of thing is often highly speculative. It should be project based, with concrete deliverables, and done with a non-permanent grant. If things go reasonably well, then there can be followup grants. This is what the STA focuses on, and is a major gap in the FOSS world.
2. Established phase: Once the software is actually ready for adoption (thanks to help from the STA!), and gets integrated into government functions, then the agencies that *use* the software should be setting up enterprise support contracts that give long-term support and stability to the projects they've adopted. A good example of this would be Nextcloud who has multiple such contracts with different parts of Germany (also other European organizations). This part is better off being done by the agency that *uses* the software, rather than having the STA do it. Some of these agencies do in fact also have internal software developers that work on Nextcloud.
I don't think it's a shortcoming of the STA that they're focused on point 1 rather than point 2, I think if they were forced to do both, they'd actually be less effective at what they're doing.
The STA is basically trying to fill the role that venture capital plays in getting a startup ready to take on customers, except the STA doesn't take an ownership stake, and they focus on FOSS.