The explanation below assumes you are familiar with
WCAP/WCOP does provide payment options that let you pay totally from WP site, but there are certain exceptions due to requirements for different types of gateways.
You have following options available if you want to have your payment processed on WP site.
1. If your payment gateway supports the use of iframes, you can open invoice in Popup window without leaving your WP.
To access invoice settings navigate to WCAP > Settings > Invoice Settings, and choose the pop-up option from Show Invoice as drop-down.
2. If you are using Marchant Gateways, you can use WCOP to stay completely on WP.
Why ThirdParty and tokenized payments are not supported by WordPress in most cases?
1. WCAP/ WCOP are based on API and do not use the road techniques to handle things. Only the methods that are available through API are implemented in order to provide a standard product.
2. Most Third-party gateways need for the transaction to be initiated from the website that is on their list.