There is a common assumption that factors are not interested in speeding up payments from customers.

This is not true because everyone knows that the longer the invoice is delayed, the tougher it becomes to collect.

What factor would want a risk such a situation? Recourse factors certainly do not prefer such a situation, since it means spending both time and money on collection. Just supposing the customer does not pay, the factor approaches the client/business owner to issue a fresh invoice to replace the unpaid one. If the business cannot do this, then the factor also suffers a loss.
Factors prefer creditworthy invoices so that they also receive their payments on time. As factoring discounts escalate over time, they prefer thirty-day terms to sixty or ninety-day terms because this means their money is guaranteed and the delays in payment only mean lower income for the factor.

So naturally, factors will always opt for invoices that pay quickly rather than those that delay because of the lower risks involved.