I've been wanting to post something about this for a while. It might be a bit controversial but even if it doesn't justify to you that Kane should take the occasional FK, it should at least explain why he does.
Did it ever strike you as odd that a player of Kane's quality is seemingly so bad at direct FKs? We're talking about a player who's at least a solid 7.5/10 in every aspect of the game; a player who can score every kind of goal from every kind of position and angle; a player who can pass and strike a dead ball with glorious accuracy. That Kane's shortcomings on FKs to date appears odd is because it is odd.
In training, he bangs them in. Watch any video of training, free kick challenges, anything outside of a match context and you'll see this. And it's not editing either: I've been lucky enough to watch him train live with England and I've seen him put what must've been almost 20 in a row top bins around training dummies. That was from multiple distances and angles, including some truly quite impressive stuff.
All of which explains why he's allowed to continue attempting competitive FKs for both Spurs and England. We may groan when Kane picks up the ball but there's a reason none of his teammates argue with him -- and it's not just respect. They've seen what he can do, at least in theory. I'm sure we all understand that transferring a skill from training into competition adds a whole new dimension to the problem.
Although, like almost all elite athletes, Kane has a suitably elite mentality and immense psychological fortitude, I'd argue that he is prone to mental blocks. When, in his second major season, he still hadn't scored after six games, his shooting was starting to become less confident, which manifested as snatched shots, miskicks, and so on.
Even back then, however, he had the mentality and underlying self-belief to know that he had to push through it somehow, so he took more shots, even if they were low-% and he wasn't striking them the way he would've ideally wanted. He kept brute forcing the issue until he finally got a bit of a lucky rebound against City. Afterwards, he never looked back. In fact, I'd argue that he's never had a problem with confidence to that extent since (because he knew he would always bounce back).
He hasn't reached the same point with direct FKs yet. He's stuck in that second-season goal rut of knowing he can and should be doing better, yet he isn't. And it's playing tricks on his mind. As for why he's having this problem so far into his career, well, he still hasn't scored an undeflected FK and he hasn't scored a FK at all for years. He hasn't been a consistent taker for any length of time either, allowing a lot of rust.
The most important factor, though, is that direct FKs, like crosses, are a very low-% scoring opportunity. The average direct FK has an xG of about 0.05 (i.e. you would expect 1 in 20 to be scored). This is how/why Eriksen was still referred to as a FK specialist years after last scoring from one. We remember the few beauties he scored, but he also missed at least 60.
With Kane, we just don't have that same successful frame of reference to reconceptualise the basic fact that missing 10 or even 20 in a row is not uncommon. But 20 is a misleadingly large number. Kane has probably taken 4 or 5 since the restart. The expected probability of him scoring from those is far lower than that of a coin flip outcome but we're attuned to expect him to miss - to be more sensitive to those misses and to have our biases confirmed by them - so we take notice of those misses when if Eriksen had also missed them all (which would've been more likely than not), we would barely have blinked.
What happened when Kane was a consistent taker at Spurs, albeit for a brief length of time? He hit the woodwork three times in just a few months (video of these is hard to come by but linked below paragraph is one against Watford). The total xG of all three FKs he came within an inch of scoring was 0.11! And during this period, he looked like a better FK taker than Eriksen! We too easily forget the time that Kane was actually forcing goalkeepers to make great saves from FKs. He was so unlucky never to score a clean one back then. If he'd rolled two dice and got anything other than two 1s, he'd have three FK belters to his name and we wouldn't even be having this conversation -- because we're reaching the central thesis of my effortpost...
I reckon it'd only take one clean, undeflected goal from a FK under match conditions to flip that switch in his head - the same one we saw against City all those years ago - and turn Kane into a serious and consistent FK threat. He could be deadly if he put the same level of ability as his shots from open play (and the FKs we know he can take on the training ground) into match set pieces. He would offer an incredibly dangerous alternative or even primary option in a team without an obvious direct taker of choice. That's clearly felt, internally, to be worth the experimentation and the technical difficulties. I agree.
TL;DR: Kane is actually good at FKs, his stats and the aura around him taking FKs are misleading, he just hasn't managed to consistently apply training ground theory to match day yet, and if he does get the chance to, he'll smash them in.
