The supposition of the SBD, as in many others of our church orders, is that those ministers laboring "in the kirk" should be provided for in a way that, as the OPC order puts it, renders him "free from worldly care."
It is, btw, not the case for the SBD, as it also not the case with any church order for an established church, that the gifts are all assumed to be voluntary, as some in this discussion may suppose. Established church ministers may be supported by state stipend in addition to the gifts of the gathered in the local church. That situation prevails nowhere in practice in the USA, of course (though it does exist in principle among some here).
It should also be noted that this is not the way that Paul received his support. He claimed the right to receive support exclusively from the saints but forwent such of his own accord. Our Reformed and Presbyterian church orders pick up that claim of right to support and thus make clear that the minister should receive such and thus be "without care or solicitude."
Much of what has otherwise been spoken to in this thread makes, at least arguably, a different point from that addressed by the SBD. I take the SBD to be addressing the ministry of word and sacrament within the institutional church. Even if the SBD sees the institutional church as exhausting distinctly Christian labors, and, as I said, this is arguable, more recent church orders have not. The OPC, for instance, does not regard all extra-ecclesiastical agencies, whether for the distribution of Christian literature, training of ministers, etc. as impermissible. I suspect that some here may, but I believe that we as Christians have freedom to form societies to publish and distribute Christian literature, to train ministers and other Christian workers, and the like.
Such societies are not the institutional church or an agency of said church, but are "non-profits" (thus not businesses seeking to make money). I perfectly understand Bruce and all others not wanting to be contacted for money by so many organizations claiming to do Christian work. But we must not mistake irritations to our flesh, and perhaps they are in every way genuinely and properly irritations, as permitting us to lay down a rule that God's Word has not laid down.
Whatever the intention of the OP--I take no issue with but fully support the SBD in its contentions--I do not think that we can from the SBD draw a rule, as some have or seem to have, that it is illegitimate for a Christian society or agency (be it Ligonier, a seminary, or whatever) to make its needs known and to ask for contributions over and above what one would and should give to the institutional church. One must tread lightly here, but if one wishes to maintain that extra-ecclesiastical Christian organizations are simply invalid, then we really should not be having the conversation on an online board that is not the church, that seeks contributions for its support and continuance, and that seeks to do certain things (foster fellowship, teach, etc.) that do not replace the church as an institution but that parallel it and that permit people of different communions and places to dialog with each other.
Peace,
Alan