Why hasn’t Tom since a bow and arrow even if it’s such a valuable weapon for one of his heroes, Robin Hood?

I'm sorry, I do not understand your question as asked. Tom did have a bow and arrow that he crafted himself.

Just here the blast of a toy tin trumpet came faintly down the green aisles of the forest. Tom flung off his jacket and trousers, turned a suspender into a belt, raked away some brush behind the rotten log, disclosing a rude bow and arrow, a lath sword and a tin trumpet, and in a moment had seized these things and bounded away, barelegged, with fluttering shirt.

And at last Joe, representing a whole tribe of weeping outlaws, dragged him sadly forth, gave his bow into his feeble hands, and Tom said, “Where this arrow falls, there bury poor Robin Hood under the greenwood tree.” Then he shot the arrow and fell back and would have died, but he lit on a nettle and sprang up too gaily for a corpse.