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You say, "My personal experience push me to say : for bells, but bells don't occupy the whole tower."
They do not have to occupy the whole tower, but for maximum effect, they have to be hung quite high - which means that you need the rest of the tower to give height to the bell chamber and - at least in the English tradition - to give enough space for efficient work on a bellrope.
So the question might be - "What other uses did people make of the towers which they needed for bells?"
Seriously, however, I suspect the most important factor is an artistic/cultural one. Most churches from the Romanesque period onward were designed not just to be a place for communal worship. They were statements about the wealth and power of the community which built them, or the local magnate who paid for them or even about the beauty which could be produced by the work and dedication of the builders (e.g. at Chartres).
The model for ostentation was the defensive structure of the castle or the great house. These usually had towers for military reasons, but that establishes towers as a part of the "building to impress" vocabulary. As you have pointed out impressive gates at the entrance to a city are not new - cities have been guarding their entrances with fortified structures with good vantage points for almost as long as there have been cities.
So what more natural, when you want "look at me" architecture, than a building which rises high above its surroundings and can be seen from miles away? It's worth it - when thinking about medieval architecture - to imagine any town and most cities as places where nearly all the available buildings were no more than 1 or 2 stories high and built of wood. Towers of stone, reaching up to God's Heaven were a powerful statement and a psychologically unsubtle reminder of the importance of that building and those who controlled it.
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Romanesque architecture It is an early architectural style characterised by thick walls and narrow windows.
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I read on wiki some old monasteries and cathedrals include conjuratories in their towers, small religious buildings from which ceremonies were conducted to bless the fields and ward off calamities caused by the weather. People believed in weather spells during the romanesque period.