A worked example makes the trade-off obvious, because the same balance can be refinanced two ways and only one of them leaves you better off overall.
Say you still owe R180 000 with 42 months to run at 16,5% a year. The instalment is roughly R5 670, and by the end you will have repaid about R238 200, of which some R58 200 is interest.
Refinance that balance at 13,5% over the same 42 months and the instalment drops to about R5 401, the total to roughly R226 850 and the interest to around R46 850. You keep close to R11 300, less the new initiation fee, which is capped at R1 207,50 including VAT.
Now take the identical 13,5% rate but stretch the term to 60 months to get the instalment down. It falls to about R4 142, which is more than R1 500 a month easier to carry, yet you repay roughly R248 500 and the interest climbs to around R68 500. That is some R10 300 more than leaving the original agreement alone, bought in exchange for cash flow today.
Both routes are legitimate, and in a tight month the second one can be the right call. The mistake is choosing it while believing you bought the first. Decide upfront whether you are after a lower total cost or a lower monthly instalment, then measure every quotation against that single goal and ignore the rest of the sales pitch.