To start, it’s not 0.65" inside diameter, it’s 0.065" wall thickness. With a fixed outside diameter, a larger inside diameter has thinner walls, which is cheaper and lighter but also weaker.
Thicker will be stiffer but it’s diminishing returns. It’s just one of several parts that can deflect, and beyond a point there is no benefit in stiffer rails but there are downsides. Stiffer tubes are heavier, which can make the machine slower because the maximum acceleration without missing steps is lower. Lower feedrates can in some cases also shorten tool life and perform generally worse.
By the time the whole thing is built, the price of increased wall thickness is not that much higher. To me it seems the 0.065" recommendation is not simply a tradeoff between price and stiffness. It’s where stiffness is not really improving and the additional weight (and cost) are not buying anything.
This balance can also be influenced by the build size. Larger machines incur a stiffness penalty that’s larger than the weight penalty, so thicker tubes could make a difference. Smaller machines are stiffer to start with and thicker tubes might offer nothing but downside in weight and cost.
For the most affordable I wouldn’t go below 0.065" but you could get mild steel (non-stainless) and keep it dry. For extra stiffness you could get stainless with 0.12" wall thickness, and while you might never see the difference, you can sleep well knowing that the rails are not the limiting factor in the overall system stiffness.