Several reasons for me.
1. Hold up play. We still struggle at times when forced to play the ball long. A physical and tall striker helps us hold the ball up and build from there instead of it just bouncing off defenders and opponents getting it. This also makes it more risky to press us high up the pitch as those long balls become more difficult for their defenders to deal with.
2. Link up play. Playing the ball into a striker facing the wrong way that can play lay offs or perhaps even turn a defender is very helpful. Doesn't have to be tall to do this, but strength is a huge benefit and height certainly doesn't hurt.
3. Crosses. A tall physical presence is more likely to be threat from crosses. Particularly the type of crosses against teams that sit back a lot and there's not going to be much space to get in behind or space to find in the box. Against teams that more or less park the bus this added ability to be a threat from crosses has real value for me at least. And it's not only the goals you get from crosses. Having players that are a threat in the air actually (imo) makes it easier to play effective football in other ways too. Full backs and wingers from the opponents can pretty much just stand off our wide players and full backs if they have no one to cross to. Give them 2-3 yards of space and back off if they get taken on. A target to cross to forces wide players for the defending teams to close our players down, that also makes it easier to go past them and create space and imbalances in opposing teams.
4. Pochettino's teams. At Southampton he had Lambert. The only striker they signed when he was in charge was Osvaldo, a player that does offer a physical presence. At Spurs Pochettino gave significant playing time to Adebayor at first, before Kane stepped up and made himself first choice. Soldado on the other hand barely had a look in as a striker and was (iirc) used just as often in one of the 3 attacking midfield roles as the striker role.
5. Other teams. Lone strikers that are "complete" seem very popular among teams that play a lone striker, and teams that play similar football to ourselves. Lewandowski was absolutely huge for Dortmund and arguably the only player Klopp lost that he wasn't able to replace effectively. In part (imo) because they couldn't find another complete striker and were left to some extent with a choice between physicality and other attributes. Simeone's Atletico Madrid team seems like a similar story. Costa, then Mandzukic, try to get the same from Jackson Martinez (though not successfully). Bielsa's Bilbao team had Llorrente when they were successful.
Yes there are teams that succeed without a physical option up front. But in my opinion it's more difficult. It requires more quality in other positions and more ball playing quality all over the pitch. Some teams are also helped by physicality in the attacking midfield roles (Yaya Toure at City for example), something we don't have all that much of. I'm not at all saying that we can't succeed without that physicality, but I would like to see us have another physical option that Kane just in case.