“If that happened in real life, that is”.
You’ve just ceded the argument here. You’ve just admitted that while this is perfectly true: that a ridicilous expenditure could be registered as legitimate GDP growth (were that to actually happen which, the fact that Keynes would have suported this idea himself aside, is ludicrous given the example but remains, nevertheless quite an astute counter)–you maintain that GDP remains an adequate tool to register genuine growth and that your original argument thus stands. But if the GDP formula cannot effectively distinguish between the two in practice (that is, between genuine growth and wasteful expenditures) and, furthermore, cannot counter-calculate the benefits that would have accrued had the money not been taxed away from private citizens to effect those expenditures in the first place, then it really isn’t evidence of the viability of your argument, is it? The confidence you demonstrate in your conclusions isn’t matched by the integrity of your supporting evidence.
If, however, you’re simply suggesting that Leftist governments spend more and that that therefore registers as higher economic growth as measured by GDP, then yes, you’re absolutely right. But who cares? If a Leftist government wants to re-pave and rationalize all the roads with a new ultra-durable concrete at a cost of $10 trillion in order to lower private transportation costs etc, then the GDP growth figure for that period will balloon long before anyone can actually demonstrate whether this is a good idea. And even if it fails miserably to bring transportation costs down because the construction costs keep rising (as is usual for budgets), well look, more GDP growth. Next, it turns out that the roads will only last half as long as expected because of the volume of traffic (the exuberance of people wanting to drive on these new roads) and the unpredictable wear of the elements. Maintenance costs have now doubled. More GDP growth!
In short: woopty-do.