Cole is a modern character and thats why he can fit well with the characters of SF and Tekken. Samus is from the future and Link is from a fantasy realm. If an exclusive character were to work, it'd have to be someone from a realistic universe similar to our own, within a modern time period.
If anyone could work the most, it'd be Little Mac.
Thats why Link fit in Soul Calibur, it's not in modern times. Kratos worked alright in Soul Calibur, but he fit more in Mortal Kombat, despite the time differences (even though Kratos is clearly from an earlier time, there are MK characters that look very similar in terms of attire and design).
Also, SF x Tekken is a fighting game and you need people good at fighting with their hands. Link and Samus are weapon users --- "Pokemon aren't just things to collect and trade like toys or dolls, you're a monster!" - Misty, Pokemon 2000