As the OP's Tele has a vintage radius fretboard, It probably has barrel saddle bridge as well, which always make setting the intonation less accurate than on a 6-saddle bridge, even with sloped saddle pieces fitted. But if the OP isn't retuning after fitting a capo, then that's probably the main cause of his problem.
Rick Beato is a great YouTube presenter, and almost always talks 100% sense (one of the few YT music channels that do). His 'what makes this song great' videos are superb. Now it may seem like nonsense that a Gibson scale length is inherently harder to intonate than a Fender scale length (I definitely wouldn't say impossible), but if you think about it, it's all about % errors and the bridge type used. Given the same ability to position each fret slot correctly (say to within ±0.1mm) and the same gauge/height of fret wire, then percentage-wise, it's always going to be easier to get the frets seated in the right position on a longer scale neck than a shorter one. And the more accurately positioned each fret is, then (theoretically) the more accurate the intonation is going to be.
A six-saddle Fender Strat-style bridge will allow each string height and length to be adjusted, whereas on a Gibson T-O-M style bridge, string length adjustment is fine, but height adjustment is always a compromise as you can only adjust the overall height at the ends. So if you want to bring one string down a bit but can't (because it would upset the action on the other strings), then it stays a bit high, requiring you to put more tension on that string than the others. When playing chords, this could mean that you don't apply enough pressure to that string to fret it properly, or you over pressure the other strings, causing them to be slightly sharp.
So yes, there are some definite theoretical benefits on intonation of a longer scale + fully adjustable bridge. But then you need to take into account all the other things that affect intonation, like player string fretting pressure, fret height, variations in fret height, fret crown position, fret crown radius, variations in string mass/unit length,
evenness of neck curve etc. and it really doesn't make enough of a difference to notice IMO.