I think you're wrong about petty/big picture here. Anaheim City Council are following a very big picture plan - The Disneyland Resort Specific Plan, adopted in 1993. It's over 250 pages, before you even enter the Environmental Impact Study or the Development Standards Chapter in Anaheim City Code. The very definition of this kind of plan is "big picture." If you read through even the big parts, it's the blueprint for how California Adventure was developed, among other things. These kinds of plans are set to be long-term visions, with rules. It's not dissimilar to how most municipalities in many states do zoning (types of residential, where you can put heavy industry, can you put a chemical plant behind a school and is the fire department in the blast radius, etc.).
This plan sets the maximum number of hotel units in each zoning district, and defines how many of those can be timeshare. The reason they restrict timeshare is multi-faceted, with a lot of it pointing to the convention area, and to the ease of booking for the average visitor.
Anaheim also have wanted to diversify the hotel offerings. The last tax credit was on offer in hopes of getting a high-end hotel group to build (not Disney) and they were not happy when Disney jumped (although they couldn't legally restrict it from Disney), or when Disney demanded things above and beyond the tax credit on offer.
It's not "petty" to want to not have one company controlling most of your hotel space, given Anaheim's goals. Anaheim are not in a place right now where the employment numbers are a concern to them, as employment is very high and available local housing is extremely low. It's also not petty for Anaheim to want to understand the benefits to them (beyond the occupancy tax). Disney aren't pitching this because they are benevolent. They want to build this because they can charge $250pp.
Disney has 11% of HOTEL rooms. That doesn't count all the motel style rooms along Harbor nor all the new rooms coming online in 2020+2021 from JW Marriott to Westin to Element.
There's no shortage of rooms and a DVC isn't going to impact that much. Anaheim probably just knows that DVC stays don't generate as much for the City as it does for the mouse.
Anaheim Resort™ District / GG 92 20,199 rooms
Within 1/4 mile of convention center 10 4,469
Within 1/2 mile of convention center 41 8,749
Hilton Anaheim 1,574 140,000
Anaheim Marriott Hotel 1,030 100,000
Disneyland® Hotel 975 150,000
Disney’s Grand Californian Hotel® & Spa 948 20,000
Hyatt Regency Orange County 654 65,000
Great Wolf Lodge Southern California 603 21,967
Anaheim Majestic Garden Hotel 489 20,000
Sheraton Park Hotel at the Anaheim Resort 490 30,000
Disney’s Paradise Pier® Hotel 481 30,000
Anaheim Fairfield Inn by Marriott 467 1,369
Wyndham Anaheim Garden Grove 384 36,000
Embassy Suites Anaheim South 375 11,000
Anaheim Marriott Suites 371 9,000