Seems like the tax rules outlaw pure barter and make you use dollars in your transaction whether you want to or not.
This is part of what it means to be a national currency -- it's what the government accepts for payment of taxes.
I mention this because you specifically call out "equivalent value to the traders".
That value is not something you can tax directly. It's more like happiness than cash. In the barter, the traders walk away with the same value of goods, but greater happiness. I'm not sure what dollar value the IRS places on happiness, but based on their behavior, I'm pretty sure it is $0 per smile.
Therefore, neither trader in a normal barter should realize a taxable gain.
In a happy coincidence for the IRS, assigning monetary values to everything makes it trivial to assign a value to the trade for the gaining party to pay tax on. Again, not relevant to what barter is.
As you say, anyone with enough cash available would always prefer settling with two trades using money instead of one barter trade. So really, the barter tax is only levied on people who don't have the money to pay it and on tax avoiders. The tax avoiders find another loophole; the poor people remain screwed.