Partly, yes. Some of the countries still play catch up after being part of or aligned with USSR up until it imploded in the beginning of the 90s.
If the EU countries were bidding against each other maybe a few exceptionally rich and small countries might have end up as Israel while others pay much much higher prices for not-better situation and the rest simply end up like Africa.
I don't think that the contracts would have made any difference in the supply. If that was the case, US could have simply be done before Trump loses election by pouring it's enormous monetary resources. I don't think that US run out of paper for contracts in the Trump era.
"The Oxford-AstraZeneca vaccine is much cheaper, although neither the UK nor the US can match the EU’s $2.15 deal: they are expecting to pay about $3 and $4, respectively, per dose."
On Monday, AstraZeneca said it will provide vaccines at cost “in perpetuity” to low- and middle-income countries in the developing world.
Do any of the Australia or EU belong to "low- and middle-income countries in the developing world"