This actually relates to an interesting larger issue. Apparently state law prevents KDOT from designating a state highway that is entirely within city limits (probably coming from http://www.kslegislature.org/li/statute/068_000_0000_chapter/068_004_0000_article/068_004_0006_section/068_004_0006_k/ though that doesn't go right out and state it clearly).
There is one exception to that rule--Interstates, which are state highways within cities.
So picture a short spur (e.g. K-891) from a bypass (e.g. US 50) to a city center. Now if the city annexes out to the US 50 bypass, K-891 is entirely within city limits and must be given to the city. But what if K-891 crosses US 50 and continues on to another route? Is KDOT allowed to keep the piece between US 50 and the city center?
In practice the hypothetical K-891 would be retained as a signed route (consisting of state highway and city connecting links joined together) only if it were a through route. That tends to apply to US highways like US 69 and US 169 but not to spur routes, which tend to have three-digit Kansas route numbers and are often returned to local maintenance as part of arbitrage against the county and statewide mileage caps. (With exceptions for metropolitan counties like Sedgwick, Johnson, and maybe Shawnee, a county is typically entitled to one state highway crossing it from north to south and another from east to west.)
Back to the original question, I suspect that the strange routings in this area are done because KDOT wants to keep the roads as "city connecting links". If US 69 were rerouted onto I-35, the old surface alignment couldn't be a numbered route, because it would be entirely within the limits of one or more cities. But by making a longer route use these streets, KDOT apparently takes advantage of a loophole in the law.
KDOT could equally well re-route through routes like US 69 and US 169 onto parallel highways which are state highways no matter what--i.e., Interstates. A length of road counts toward the mileage cap only once, no matter how many designations are on it. For this reason the total amount of state highway mileage tends not to be greatly different whether numbered routes are left as city connecting links or are transferred to Interstates.
These routings tend to be worked out within the context of intergovernmental agreements. Although city connecting links are not state highways, KDOT has significant involvement with them through the KLINK program. KLINK resurfacing plans go out with KDOT face sheets and KDOT drawing chopblocks, and I am sure KDOT participates financially in them as well, though I don't know the grant ratios that typically apply. KLINK relieves localities of the special costs of catering for through traffic. Since KDOT contributes to KLINK, it can require that state routes be maintained to a consistent standard through cities ("he who has the gold makes the rules" and all that).
In some cases the local agency may think it is in its best interests to have some of its surface arterials within the KLINK program rather than to try to finance ongoing resurfacing and other rehabilitation through the usual funding mix for city streets (local property taxes, often a local sales tax increment, and a block grant for street improvements which is partly financed by fuel taxes and license fees and is doled out by county and city). In other cases it goes the other way and the local agency sacrifices KLINK eligibility in exchange for KDOT financing capital improvement elsewhere. I believe this happened with the surface-street routing of US 24 in Kansas City, Kansas, which has now been vacated in favor of moving US 24 onto I-70--I think KCK got the Kansas Speedway improvements in return, but Richie will have the details.
The funding distributions involved are fixed by statute, so typically both KDOT and the local agencies have a reasonably precise estimate of the tradeoffs involved in holding onto KLINK mileage versus giving it up in favor of capital improvements elsewhere.