Doubling down on being wrong, alrighty then.
That $14,000 income earner who pays no income tax. Let's assume they spend a total of $500/month on rent (clearly with roommates etc). That's pretty frugal, and uses up $6k per year.
According to a Dalhousie study (
https://cdn.dal.ca/content/dam/dalho...23_Digital.pdf)
A Canadian woman aged 19-30 spent $3564 on average on groceries in 2022. Food price inflation has been high so I'd expect 2023 to be more, but we're assuming someone who is both low income and very frugal on zero-rated items here, so lets assume only $3000/year of groceries. That gets our hypothetical low income person to $9k per year in zero rated/exempt supplies.
I'm also neglecting possible expenses that are exempt or zero rated in other categories (public transit, feminine hygiene products, bank fees) that would bump that number up.
That leaves them with $5k per year to spend on taxable goods and services, on which they'd spend $250 in GST and receive the $467 rebate.
If the GST doubled, they'd spend (at most) $500 in GST and receive a $934 rebate, being better off per year by $217. An extra $217 matters to someone at that income bracket.
In terms of interest, if we assume they borrowed to pay the first quarters GST at the maximum legal rate of 32% and then used the first quarters rebate to pay the second quarters GST and so on, they'd have $125 of high interest debt in perpetuity. That would add $40 in annual costs, making the net benefit to that person $177 per year.
Anyway, I'm curious which of my assumptions you think are wrong here to justify someone at this income level being worse off under a higher consumption tax/lower income tax regime? Because I can't see how spending less on food and shelter is very likely...