You already have one of the reasons, which is an uncontrollable exotherm, but there is also risk of effervescence. That can either be because the exotherm causes the solvent to boil over, or that a large amount of gas is produced at once.
You should note that if there is enough solvent (as is usually the case) and you have a condenser, the heat of reaction will cause it to boil thus keeping the exotherm under control.
On scale (kilo-lab or pilot plant or production plant) reactions are frequently run this way. You cannot exceed the BPt. of the solvent at atmospheric pressure.
Adding something drop-wise keeps things nicely under control, allows immediate reaction i.e. the reaction is addition controlled and will stop if the addition is halted, prevents side reactions, stops accumulation of dangerous amounts of reactants/intermediates and so on.