For whom are we to pray?
The second argument for not reading Calvin's "all" as "some of all kinds," is Calvin's view of whom we are to pray for. In 1Timothy 2:1, we are commanded to pray for all men. All men? Or all sorts of men? Let's do a comparison of John Gill, a hyper-Calvinist, with Calvin.
Here's a snippet of Gill's comment on verse 1:
[G]giving of thanks, as well as prayers, are to be made for all men; but certainly the meaning is not, that thanks should be given for wicked men, for persecutors, and particularly for a persecuting Nero, or for heretics, and false teachers, such as Hymenaeus and Alexander, whom the apostle had delivered to Satan. But the words must be understood of men of all sorts, of every rank and quality, as the following verse shows.
~Gill, Commentary on 1Timothy 2:1
Now compare that treatment with Calvin's:
And thanksgivings. As to this term, there is no obscurity; for, as he bids us make supplication to God for the salvation of unbelievers, so also to give thanks on account of their prosperity and success. That wonderful goodness which he shews every day, when “he maketh his sun to rise on the good and the bad,” (Matthew 5:45,) is worthy of being praised; and our love of our neighbor ought also to extend to those who are unworthy of it.
2 For kings He expressly mentions kings and other magistrates because, more than all others, they might be hated by Christians. All the magistrates who existed at that time were so many sworn enemies of Christ; and therefore this thought might occur to them, that they ought not to pray for those who devoted all their power and all their wealth to fight against the kingdom of Christ, the extension of which is above all things desirable. The apostle meets this difficulty, and expressly enjoins Christians to pray for them also.
~Calvin, Comm. 1Timothy 2:1-2
If we compare the two approaches, Gill's and Calvin's, we see a diametrically opposite view with respect to wicked rulers. Calvin says to pray for them, and Gill says not to. And notice that Gill justifies, in part, his treatment of wicked Nero by saying that we are not enjoined to pray for all men, but "men of all sorts." Calvin could have used this logic as well, but didn't.
There are two things to be noticed here: first, Calvin might have used the same justification that Gill did for saying that we need not pray for wicked Nero. He might have said that we are not enjoined to pray for all men, just all sorts of men. He certainly had the analysis suitable to the task:
Hence we see the childish folly of those who represent this passage to be opposed to predestination. * * * They might have had some ground for saying this, if Paul were speaking here about individual men.... * * *
But I say nothing on that subject, because it has nothing to do with this passage; for the Apostle simply means, that there is no people and no rank in the world that is excluded from salvation; because God wishes that the gospel should be proclaimed to all without exception.
~Calvin, Comm. 1Timothy 2:4
Calvin set up the possible distinction between all individuals and all sorts of individuals. Admittedly, the Calvin quote above is from verse 4, not verse 1; but the reasoning is identical and if it applies in verse 4, it would be equally applicable to verse 1. But Calvin did not use that justification. Rather, Calvin said that our prayers ought to include the wicked rulers.
This comparison ought to show us that Calvin did not mean the same thing as Gill when he distinguished between "individuals" on the one hand, and "people" or "rank" on the other. For Calvin, the idea of "all sorts" excluded no one, while Gill used the idea of "all sorts" to exclude wicked Nero.