Actually, dual-stacking a website has some benefits. In some countries the CGNAT boxes tend to be oversubscribed and introduce latency. Apple has observed that too and presented some numbers to developers. Having two protocols can introduce redundancy for those that support both. If there is some routing issue e.g. because of some cable cut most clients will automatically use the faster protocol.

If you run some infrastructure, you have to dual stack only at the gateway to other networks. You can run IPv6-only or IPv4-only inside and reverse-proxy or tunnel the traffic. Running IPv6 only can save you some money in the cloud today, it is not much but for small things the charge can be in double digit percent.