Question

why the induced fit model is more widely accepted than the lock and key model

Answer 1

Induced fit theory is the most widely accepted and used. Induced fit is themost accepted because it was a development of the lock and keymechanism as it suggests that the enzyme's active site changes slightly so that the substrate can fit, whereas the lock and key says nothing about the active site changing.

Answer 2

Induced fit is the most accepted because it was a development of the lock and key mechanism as it suggests that the enzyme's active site changes slightly so that the substrate can fit, whereas the lock and key says nothing about the active site changing. So, substrate enters active site to form an enzyme-substrate complex, active site changes, substrate released to form an enzyme-product complex. 
The lock and key mechanism suggests that the substrate is complementary to the active site, so both theories have value but the Induced Fit theory is more reliable and valuable.