Some advertisements recently give the impression that you can "Demat" your mutual funds! Yippee! So you should buy through a stock broker on an exchange!
But this is a stupid reason.
Mutual funds are "dematerialized" anyway.
Materialized means that the unit certificate that you have is the be-all and end-all of your ownership; in the past, shares were sold as certificates. When you sold, you gave your certificate to the broker, who would find a way to get it over to the new buyer. If you lost your certificate, you were in deep doo-doo. You had to file an FIR and hope you had a photocoyp and beg and plead and offer your children as guarantee to get your shares back. Many instruments - NSCs for one - are like this.
Dematerialized means what you get in paper is an account statement, that your holdings are really maintained electronically. If you lose your statement, no big deal, you just call them and they send you a new one. You might need some details, but usually they can find your holdings with a PAN number nowadays. Shares are now usually held in demat mode, with demat "depositories" like NSDL and CDSL accounting for a major part of all share holdings in India.