Did covid-19 vaccination lotteries backfire?

Connecting vaccinations to lottery prizes doesn't seem to have worked too well:

Ohio, the state that launched the national movement to offer millions of dollars in incentives to boost vaccination rates, planned to conclude its program Wednesday — still unable to crack the 50% vaccination threshold. …

In late May, Oregon Gov. Kate Brown announced that Oregonians who are 18 or older and have received at least a first dose of Covid-19 vaccine will automatically be entered to win $1 million or one of 36 $10,000 prizes — with one winner in each county. Oregonians, ages 12 to 17, have a chance to win one of five $100,000 scholarships. …

The Oregonian reported in early June that the seven-day average of adults receiving their first shots had actually decreased from about 9,000 the day before Brown, a Democrat, announced the lottery to 6,700 nearly two weeks later.

In Colorado, vaccinations have slowed since its lottery was rolled out by Democratic Gov. Jared Polis last month, with about 589,000 fewer doses given out in the month since Polis’ announcement, compared to the same amount of time a month before the contest began.

Could the lotteries have backfired by implying that getting vaccinated isn't intrinsically desirable, hence the need to entice people by giving away millions of dollars? In other words, the financial incentive (a chance to win the lottery) could undercut the non-financial incentive of getting vaccinated (including virtually eliminating the risk of death, at least for now). 

There was no controlled experiment with the vaccination lotteries, so we can't know for sure what effect they had. But what happened could be analogous to the Israeli day care experiment described by Freakonomics, where a financial disincentive (a fine for parents who are late to pick up their kids at day care) undercut the non-financial disincentive (parents wanting to avoid feeling guilty for inconveniencing the day-care workers). That was a randomized controlled trial where the fee was introduced at some day cares but not others, and the result was that about twice as many parents were late at day cares that did fine them!