What are the consequences to replication of having a replication machinery with no 5’->3’ exonuclease activity?

The exonuclease activity can be also described as ---5'-to-3' exonuclease (Nick translation activity)

This enzymatic activity that is 5'-to-3' exonuclease activity plays an essential role by removing RNA primers during replication. This process is similar to nick translation , the simultaneous polymerization in the 5'-to-3' direction from a nick with concurrent removal of nucleotides ahead by the 5'-to-3' exonuclease activity.

So this helps in making the extension in a smoother way with less error incorporation

5'-3' exonuclease activity is an repair strategy used DNA polymerase I. the polymerase would move in the forwards direction and excise the miss-matched nucleotides at any position . This mechanism is used in case of UV-mutation where the strand gets mutated due to UV and in turn the strand is deformed.

One example I would give which I used in my lab is this ---T7 Exonuclease enzyme

This T7 Exonuclease acts in the 5' to 3' direction, catalyzing the removal of 5' mononucleotides from duplex DNA. T7 Exonuclease is able to initiate nucleotide removal from the 5' termini or at gaps and nicks of double-stranded DNA