Is combining features deemed 'important' by different learning methods logical?

I apologize for the post's title, but hope to explain with an example.

I have a simple binary classification problem involving hundreds/thousands of features to predict cancer. Given the field, a panel of features to predict cancer is preferred as this is considered more robust across the population, and moving forward, the panel will get smaller as classifiers are qualified in larger studies. Point being, the object is a small but not overly small panel of features (<20 or so).

Using different supervised learning approaches (SVM, random forest, neural network, etc.) combined with sequential feature selection (minimizing mis-classification error with forward feature addition to models), I can create classifiers using a subset (panel) of features. The models won't always find the same features, though there will be overlap.

In this example, does it make any sense to use all of the features selected by all the classifiers to move forward? OR is the only rational choice to chose one panel of features and their classifier and move forward to qualify in a larger population?

Please ask any questions for clarification or let me know if you think finding a consensus panel by machine learning is idiotic.

Thanks