Well, IMHO you both have points. The 5/64" ring sets have been in use for decades now and are well proven. If they work for you and you are happy with using them, have at it and carry on.
Modern technology and materials has enabled the ring widths to be reduced for lower friction in the engine which equates to more power and fuel economy. The General went to 1.5mm rings on their LS engines which is very close to 1/16" ring width. NASCAR is down to 0.5mm compression rings. That is about 0.020" ring width. That is almost like using oil ring rails as compression rings. Those teams are chasing every 1/2HP everywhere they can find it.
For a new build looking to modern rings could be of benefit. Some aftermarket LS off the shelf pistons are now machined for 1.2mm, 1.2mm and 3mm ring sets. If you find a piston with the chemistry, piston top design and compression height you desire, use it and the rings it is machined for. 1/16" or 1.5mm are likely the same cost as 5/64". Also consider ring weight as a factor when racing. As you get progressively narrower rings the price seems to get progressively higher as you get narrower than 1/16".
For my Ford 289 I found pistons that take 1.2mm, 1.2mm, 3.0mm rings. Total Seal makes a zero gap top set that will work. The issue is today's cost delivered to Canada for pistons and rings is about $1700 CDN. But then I do not foresee ever having to air out this engine again.