Dropping off at a depot is not really how this bit of the industry works – the courier collects from the distribution centre in almost every case.
The issues with doing your own drop offs include: finding a new courier, booking, figuring out a collection time which then impacts your shipping estimate cut-off time, and paying for this whole service.
In terms of price, you're going from a high volume commodity service at typically a crazy low price for courier shipping (for what it is), to adding a new additional short-term, lower volume or unproven volume, from one of the smaller providers who aren't operating at Fedex/UPS scale. I could imagine this doubling shipping costs, which might be untenable for many ecommerce businesses.
In terms of the actual logistics, it's a challenge, plus typically this would be automated – your software will do this all for you. Now your software needs to book and pre-advise a new provider? And track through them? But also track through the original one?
For most businesses it's probably impractical to implement this, and for most that could they probably have contracts with the couriers that mean they won't be hit by this or they do their own deliveries. I think the space in the middle is a pretty small subset of companies.