If it’s a TH350 trans, no kickdown cable means the trans will short shift at WOT. It won’t technically hurt anything just won’t perform as well as it could.
If it’s a 700 (based on your discussion I’m guessing that’s the case) running around with the TV cable adjustment off will damage the trans eventually.
You didn’t mention what carb you installed, you may need to get the proper linkage to set the cable right. The TV cable adjustment needs to be correct, “close enough” ain’t gonna get it! It’s also not enough for the cable to simple be tight at WOT, the TV cable range of motion is designed to gradually raise line pressure as throttle angle increases. Just because the cable is tight at WOT doesn’t mean the pressure is right at less than WOT. This is why you hear so many horror stories about people who can’t get their part throttle shifts correct. If the pressures aren’t high enough, 1 or 2 sloppy sliding shifts will be enough to permanently glaze the clutches or band. It’s all downhill from there.
ideally, a line pressure gauge is needed. Any oil gauge that will read to 300psi is good. You need around 90psi at idle, slowly pull the tv cable, it should go up to about 250ish, depending on the valve body calibration. It’s common to see the pressure flutter with the engine at idle, but at a slightly elevated idle speed it should be pretty steady.
Hope that helps.
