Its all about customer experience and fulfilling the delivery promise. For me Delivery is as important as the product. I will abandon a shopping cart if the delivery options are not satisfactory enough and purchase elsewhere.
Our customers tell us they have gained double digit growth by removing the static delivery page within their website.
Instead they have dynamic delivery options provided by us to enable them to communicate in real-time the delivery options available to the consumer.
This is based on order attributes, delivery service availability, time of order, cut off, delivery location etc etc.
This brings together the warehouse with the web front end. Meaning accurate delivery options are provided in real-time fulfilling the customer promise and never mis-calculating delivery for the retailer.
In answer to your question - it is important to provide choice. If a consumer has a choice to have it tomorrow at a premium, but see they can save by having it in 2 days... this may be a better experience for them...
Remember next day/Same day delivery is not always the best.... The best is to give the choice in real-time of what you can actually delivery and promise.
By doing this it opens a world of possibilities, not just for the consumer but also for the retailer.
If you have any questions about this, please get in touch with me.