You can make LTC based completely off talent and hard work.
COL takes talent and hard work, and a combination of luck, timing, and political connections. The more talented and harder you work, the less the other factors are required -- but they still apply.
Making General requires all of the above to an extreme degree -- especially luck, timing, and political connections.
It also takes a steadfast determination to sacrifice your personal preferences for what Army Senior leaders want/need you to do.
There is no bureaucratic organization on earth where you can rise to the senior ranks without political connections. That is how human society works. The Army is no different.