Oh.. 21 years? That's so good to hear. Congratulations to you and your wife. Someday, I want to boldly say this also.
Marriage is a loving concept since time immemorial and so will it remain till the end of time. it is forever relevant

Do people in a relationship need to get married and if so why?

Yes, they really need to eventually if they wanted something more and remain committed to that special person for the rest of their lives. The bond makes the relationship stronger, the ties makes it deeper and unique. Even For the purpose of proper procreation and children upbringing, where both parents contribute their own quota in showing their wards love

Should people get married for tax benefits, moral reasons, religous customs, etc? Or is just being a committed couple enough and there isn't a need for that piece of paper?

People get married for different reasons and there can be hundreds of valid reasons be it religious customs, moral reasons etc. But what
will keep them going for so long is their deliberate commitment and love to one another.
Although people can get divorced easily. Alongside commitment that piece of paper is somewhat necessary. It is just a physical reminder of the legal bond between the couples. It's like a degree certificate received even before you start the courses.
Once again, Happy married life