Part of the reason is that it does not fit the symbolism of the other two ordinances--both of which are pictures of the gospel. Death, burial, resurrection
I've heard this argument before, Tom, and it seems to be a bit circular: Baptism and the Lord's Support are defined as ordinances, and thus they become the litmus test for other ordinances. However, if you
a priori decide that feetwashing were an ordinance, you could reconstruct common symbolism around those three just as easily.
Not all Primitive confessions recognize feetwashing to be an ordinance on the same level as baptism and communion; some do, while others say it is an example to be followed, which has the practical effect of making it an ordinance.
Now, I am not convinced that it is an ordinance in the same way that baptism and communion are, but I think you can make a case for it, especially as an essential element of communion, which is its historical context.
It is also true that Baptists have not universally limited the number of ordinances to two; the Philadelphia Confession, which was widely influential in the 17th and 18th centuries, went so far as to make hymn singing an ordinance.
We believe that ... singing the praises of God, is a holy ordinance of Christ, and not a part of natural religion, or a moral duty only; but that it is brought under divine institution, it being enjoined on the churches of Christ to sing psalms, hymns, and spiritual songs; and that the whole church in their public assemblies, as well as private Christians, ought to ... sing God's praises according to the best light they have received. Moreover, it was practiced in the great representative church, by ... our Lord Jesus Christ with His disciples, after He had instituted and celebrated the sacred ordinance of His Holy Supper, as commemorative token of redeeming love.
Benjamin Keach considered not only baptism and communion but also preaching and prayer to be ordinances.