I think you are overestimating the support the national federation gives to its athletes. Most of the time they are on their own. She will likely still retain her club coach and continue to train in Canada (or maybe move to the United States).
There are two major reasons why an athlete changes nationality, they either had a huge disagreement with the old federation or the new nation has enticed them to switch sides. We don't know which one is the case for Sanchez, but she'll have the potential to be a big star in the Philippines if she can win golds at the Southeast Asian and Asian Games next year while in Canada it will be tough for her to get the spotlight.
Yes she's giving up winning more relay medals, but she already has 2 Olympic and 6 World Championship medals so I don't think she will regret it. She also has a chance (albeit a very small one) to win an individual medal which again will be much bigger for the Philippines than Canada.