Can you explain how V isn't going to make a difference? The statement that adding more people to the trades is going to have a crowding out effect strikes me as economically naive.

On the surface it seems like you're arguing that there is not enough room in the trades for more tradesman. However adding a good chunk of people to the trades will increase the velocity of money in the form of more people spending more dollars based on their higher salaries. The alternative is that the demand for trades is fixed, which doesn't make much sense to me.

Adding more tradesmen will not increase the demand, and so will not result in any increase in the velocity of money.

The demand for trades may not be fixed, but it is not proportional to the number of tradesmen. Most likely it's proportional to overall economic activity in some way. Doubling the number of tradesmen will not double economic activity across the whole economy, or likely have any significant impact on demand for tradesmen, so the value of tradesmen will drop until some are forced out and an equilibrium is reached, probably not far off where it is now.

Increasing the wage of people who would otherwise earn far less will absolutely increase the velocity. It's preposterous to say that it would be one to one, I never made any such claim. However, your argument is that we are somehow at a perfect equilibrium with tradespeople. That's just not the case. I feel like you're throwing your lot in with freshwater economics which has a pretty terrible track record.

Ok - fair point about the increase in velocity. But the increase in velocity will be distributed across the whole economy, and therefore of minimal impact on the tradespeople, whose value will be diluted in proportion to the supply.