Use of https://gastoken.io/ - positive or negative for the network?

I’m inclined to say it’s positive on net, for exactly this reason:

So we can expect that overall gas prices will spike a bit smoother than seen historically and owning gas tokens will further reduce that risk.

The marginal social cost of gas usage does not change 10x day by day the way gas prices do. Therefore anything that reduces the volatility of gas prices reduces deadweight losses considerably (note that because deadweight loss is quadratic, this is true even if average gas prices are mismatched to the social cost in an absolute sense; you can do the math yourself to confirm this).