1. The price of oil won't necessarily go up from here. If it goes to $5/bbl, that will make governments look a bit stupid when they filled every storage space available at $15/bbl in the open market. One scenario where price doesn't increase would be if there is destruction of demand for commuting, as people realize they can work from home just fine in the long term. Another would be if auto prices increase due to automakers shutting down production lines. A third would be if vacation travelers are still spooked by residual outbreaks after travel restrictions are lifted. On the production side, we haven't seen the kind of capitulation that would be required to change the who's-who of the market; the fracking industry has yet to go over the precipice and there's no sign of renewed OPEC+ cooperation, so there's no organic reason yet for prices to increase.

2. Strategic reserves are generally in salt domes and other accessible underground formations, so there is actually a cost to filling them and also to pumping them empty. And you can't exactly "double capacity" without buying old wells from corporations. So what you are proposing would actually be a bailout for oil producers.

3. Petroleum reserves are not terribly useful to the economy, aside from two particular cases: war and natural disaster. In war, supply chains get interrupted and fuel demand goes up. In natural disasters, production and storage can be interrupted. Outside of those two things, the ability for frackers and other high-cost producers to come online and sell oil will naturally act as a resistance to skyrocketing fuel prices in times of supply shock.

4. This could be a massive moment for renewable energy; goods transportation costs are very low and many people will be seeking work once the pandemic abates, so the government could establish WPA-style programs to build wind farms, electrical grid improvements, and solar farms -- instead of spending that money on buying fossil fuels in order to pump them back into the ground. Instead of spending money in an attempt to cling to fossil fuels, we could use this moment as an opportunity to pivot.

5. The sooner the price of oil bottoms and a few overextended frackers devalue themselves by selling at a loss in order to generate cash flow, the more likely it is that Saudi Arabia will be satisfied with the results of its price war and will return to the negotiating table to re-establish output curbs. If you try to artificially boost the price by buying crude, all you will end up doing is delaying the natural solution. Low prices solve the problem of low prices, by pushing many market participants out of the supply side and allowing the survivors to push up prices again in an attempt to capture their larger market share at a price point with a favorable profit margin.

6. Strategic petroleum reserves aren't that big, and many of them were already quite full prior to the selloff. Even the US SPR had only enough capacity to absorb all Saudi production for less than two weeks.