What you're missing is that it's a City of Austin operated enterprise, so it will be neither simple nor quick...
Would have made more sense to start the gate numbering at 10 when the airport opened, since the airport was built with expansion in mind. But the City of Austin lacks foresight in planning, and it shows not just in the airport's gate numbering but also the city's roads and highways.
When the airport opened, even the most optimistic projections suggested that an expansion of this size wouldn't be needed until the middle of the next decade. Renumbering the gates really isn't that
much of an inconvenience; they're just going about it strangely by doing it in increments (and I'm sure there's a reason. I'm equally sure no one will ever tell us what it is).
Some of the groups involved in the gate renumbering; Planning & Engineering (both project management teams for terminal improvements, and terminal expansion), Building Maintenance, Finance, and work order management, ATC, Airside Operations, Terminal Operations, Security, and IT.
Some of the issues include; gate management software and the ability of staff to make dozens of changes to 25 numbered gates already in use, work order management and the ability to make changes to thousands of assets that are related to a given gate number, the fire alarm systems and the ability to make sure a given detector or pull station is accurately addressed to a location in the terminal (you don't want the fire department running to the end of the building if Gate 25 is no longer there), access control systems, environmental control systems, accounts receivable and the ability to differentiate who gets billed for what space, coordination with fourteen airlines so they know what to communicate to airlines and when, timing for changing interactive maps in the terminal, updates to the airport web pages, and the ability of the contractor to make changes to numerous signs. That's not even a comprehensive list.
Also, keep in mind each gate has several numbered signs; a blade sign in the concourse, a four sided sign over the podium, one over the boarding door, a three sided sign at the end of the bridge, a sign high on the side of the building, and a painted number at each lead-in line. Then there are numerous directional signs that point passengers to the correct gate.