alot of DG's can easily destroy towers without taking much damage.
Torchbearer's fireball outranges towers.
Queen of Thorn's Uproot outranges towers. she also has minions and a shield that can easily absorb hits while she wails on the tower.
Rook can literally eat towers. his trebuchet also easily destroys buildings at no risk to Rook.
Regulus can snipe towers from beyond their range.
and yeah, Beast can Spit on them and run away.
whats the big deal? there are alot of ways to hit towers. you can also just wait for a wave of creeps and then run in after its targetted the little guys. Rook is good at doing this as he can keep up his own creeps for some extra time with buffs. Erebus and Sedna are good at this tactic as well.
the Beast is not at all a jack of all trades. its actually an extremely narrowly focused Melee DPS class. it really has very limited utility of any kind in terms of assisting the team. Beast just does alot of damage, thats basically it. he's got some debuffs and DoTs but everything is focused on ganking DG's and maintaing very high DPS with melee attacks.
the fact that you found one damage ability that can also be used against towers, in a manner that is roughly analagous to many other damage abilities in the game, doesn't even come close to being a convincing argument for overpowered.