There is more reasons for it.
The most important is schedulling. The KHL has similar schedule as the NHL, playing every day, travelling a lot. The CHL plays their games during IIHF breaks when SWE, FIN, RUS, CZ NTs play their tournament. So, if SKA played the CHL, half of a team could not play the CHL, because they are in NT. The KHL has said many times that they are ready to play one or two games with CHL champion, some series between CHL/KHL champions. But the CHL has refused such an idea all the time. Who is to blame?
Another aspect is financing. CHL clubs are in red numbers, why should the KHL support such a tournament? If there is no hope for a profit? You to know, CHL prize money is 1,5 million EURO and they plan to have 3 million EURO in 2022 or something like that.
Nobody cares about Euro hockey in Russia. CHL has very low attendance, but if SKA comes to some Euro CHL city, it would be sold out. So only a benefit for the CHL, not for the KHL.
CHL is de facto run by Swedes who (I mean their federation) are the biggest KHL haters. So, the KHL should support the CHL product, but Swedes (& other Euro federations) will do everything possible to stop KHL´s expansion to Europe? That are benefits for both sides? I do not think so.
I think these are the most important reasons for the KHL not being part of the CHL. And it wont change in near future. On the other hand, it seems the KHL will invite Euro clubs to the KHL preseason tournaments since next summer. This year HC Davos was invited to Astana´s tournament. If there is no interest from European federations or the CHL, the KHL can invite some Euro teams... case by case, it is more effective to negotiate with one club than one organisation (more interests from various sides).