We modify Merkle-Damgård construction by setting $z_0:=L$ (the length of the message), computing $z_i:=h(z_{i-1}||x_i)$ for $i=1,...,B$ and defining $H(x):=z_B.$ Is this construction collision-resistant?
I think that it can not be collision resistant, because by adding the input length in the beginning after many steps two different messages may have the same output, but I can not find a counterexample to refute the assumption.
Collision resistant definition (from Katz&Lindell Introduction to Modern Cryptography): it is difficult to find $x$ and $x'$, with $x \neq x'$ such that $H(x)=H(x')$.