It depends how Aguero scored the header goals. I have already explained that Lukaku scored those headers and other goals from crossings by just standing in the box and out-muscle defenders, so that means his strength and winning headers have been his main assets for him.
Which is what I said, scoring headers depend on lot of factors. Winning header at half way line is completely different.
]The hoofed ball isn't the main issue, we don't play hoofed ball at half way in all our games so far against top 10 sides this season, you are judging our playing style based on one game only against Spurs. We have played football with our feet in a lot of games and Lukaku has failed to score in those games. Positioning & his movement have been the issue for him, he doesn't give option for our midfielders or attacking midfielders to give him service. Even when we give him through ball, his run timing always late. No intelligence at all, all he expects is waiting & receiving the ball straight to him instead of trying to make a lot of good run and find his space.
You look at an example of our former goal poacher who isn't technically top class like Chicharito, the guy knows and loves to make run, find space and give option for our players to give him service. Sir Alex mentioned in his book that in 12/13 he wants his midfielder always go for early pass to split the defense by getting the best out of RVP's mobility and killer instinct. Spurs first goal basically sums up the mobility of Kane, straight kick off, Kane made the run, early pass from Vertonghen and basically split our defense. You look at Lukaku, he's not mobile enough, as a result our players can't give him early passes and defenders found it easy to mark Lukaku.
And players who aren't mobile like Zlatan last season & Berbatov at least technically top class. While Lukaku are both not technically top class & not mobile. Which makes things difficult for him.
I'm talking about games against big teams and particularly this game and how much we just hoofed it.
Re other games, Lukaku was involved in lot of moves and build up play. Check his thread, how many people started to appreciate his link up play in recent games.
Re Chicharito, he never played as lone striker. The way we play under SAF was completely different, I agree Lukaku can do more in terms of movement but aimless hoofball won't help our team at all.
Also you mention Zlatan, how many times we played the ball to his feet against big teams? Zlatan was superb that he made something out of it few times but the issue was same even last season. Against big teams away from home, we sat deeper and just played long balls which means possession was lost and we were under pressure again. Nothing has changed with Lukaku in this set up.
Also not sure how he can position himself to receive the pass when many times midfielders just played long ball from defense and hoped everything is fine. Some guy on Reddit even made video on every single pass Lukaku received, there is no way Lukaku can hold up the ball when they just hoof it.
Re bold part, I have posted how many aerial duels Lukaku was involved in other thread, you can check it. Against big teams, our team lack balls to build up play, they look for easy route out especially away from home.