Wouldn't that expose more of it to oxygen and thus increase the fire's strength?Yes, but there really isn't much else in the way of practical choices. If you had some 100% bullet-proof way to seal the fire off from any oxygen, then eventually it would go out and cool below it's ignition temperature. But "bury it in sand (or concrete)" isn't a practical solution for the average fire. Beyond that, you could play around with piercing nozzles and more wetting agents / foam and what-not and try to avoid digging the pile up, but generally speaking those things would be too time consuming for the typical fire department.
Consider that any time you're on a call, that apparatus and crew are not available to respond to other, perhaps more urgent, calls. So fire departments typically try to avoid spending excess time on the scene of a relatively low hazard fire like a mulch pile. You can't just ignore it completely, because embers from that fire could then spread and cause another fire, etc. So you have to show up and deal with it, but you want to get done as soon as possible.
A private / industrial fire brigade might take a different approach, because they are operating under different constraints.
All of that said, there is one particular case where "bury it in sand" might be used in a setting that a typical municipal FD might run into. That case would involve a Class D (flammable metals)[1] fire. Those are notoriously hard to extinguish and "bury it" is a valid option. So if a FD had some industrial areas in their district, where a factory was, say, making something out of magnesium or another flammable metal, and somehow managed to catch a load of the stuff on fire, it's entirely possible that the response would be "Call in DOT (or whoever) and have them bring a couple of dump truck loads of sand to the scene". There are specialized fire extinguishers for this stuff[2], but they're expensive, only contain so much extinguishing agent, and aren't - in my experience - commonplace on fire apparatus.
In practice, this situation doesn't come up terribly often. And a plant or factory working with lots of flammable metals in high volume might well have a private industrial fire brigade that specializes in fighting those fires.
[1]: https://en.wikipedia.org/wiki/Fire_class#Metal
[2]: https://www.monroeextinguisher.com/product/ansul-redline-30-...