Why would elf want to be a templar? You know a member of a military order directly controlled by a system of faith that encourages and condones the discrimination, oppression, impoverization and cultural destruction of the elven people both within and outside of the Alienages?
Because the Chantry doesn't encourage or condone it.
The discrimination, oppression, and impoveration is the work of the secular states and societies they live in and around. The cultural destruction, past the conversion to Andrastianism, is the result of the elves themselves letting go of the culture: fewer and fewer care, rather than anyone else demanding they forget/not practice/destroy their alienage trees.
The Chantry is explicitly open to elves, and is now actually one of the more progressive groups in terms of their value (all are equal in the eyes of the maker), the importance of approaching and involving them (the Chant to all corners of the world), and in being willing to service them and include them. The Chantry isn't the Elven patron organization, but it isn't the source or instigator of discrimination and has friendlier policies than many, even if many of its membership are themselves bigoted.
An elf not being a Templar of note is more likely to be for the same reason an elf being a Ferelden soldier of note than out of a Chantry dogmatic prejudice. Relative numerical presence, general social ostraciziation and racism, and similar factors. There are elves in the Chantry heirarchy, allegedly, and the Devs have indicated elves are somewhere in the Templars as well- just not put into the spotlight (yet).