Rugby will change, yes, but the days of 16 stone props are over. The forwards of the 60's and 70's were much smaller men because they weren't full time professionals and the sport science was just not there yet. In those days 18 stone was gigantic. Nowadays that's par for the course.
As mentioned, you need only look at Cian Healy to see the prototype physique for the modern prop. He's nearly 18 stone and I challenge you to call him fat. France already field the smallest props at international level and even they never dip below 17 stone. In fact if you look at current trends the props are getting bigger. The French have recently fielded positively massive props at the u20 level and with the success of the likes of Carl Hayman, Dan Cole, and Soane Tonga'uiha, big lads of 6'2" and 6'3" are being encouraged to play prop rather than the back row.
While your father might be right that the speed of the game will increase, the nature of the set piece and strength of professional athletes dictates that huge men will always be required at the highest level. If South Africa is going to churn out forwards of the likes of Eben Etzebeth (6'8" 19st) who are fast as well as massive, the rest of the world must keep pace.