The Fed will reinstate the USD as reserve by NOT easing. If there's money to be made, people will fight to get their hands on it. The heuristic of "always assume inflation" has worked fairly well for your entire life so far. But, like any heuristic, there will be times it breaks down.
Yes, if the Fed were to instill restraint, the USD could remain the global reserve currency. However, that turns into a situation of the Fed against congress, the presidency, and eventually most of the world.
It isn't enough to look at what the Fed alone can do, but what other comparable forces are in play. The Fed has to fight immense demand for lax policy coming from several directions or wind up deflating the economy too quickly, pushing it toward a Greek scenario - or worse.
Maintaining fiscal responsibility requires effort from multiple parts of the US government, corporate America, the domestic population, and
other nations' governments because of the reserve currency status - not just the Fed. Monetary policy can restrain to an extent, but there's arguably more pressure from other branches to continue profligacy, in addition to public outcry demanding short-term relief without understanding the consequences.
While the possibility
exists for austerity/restraint, and it may be implemented for some period of time, it is not the most probable
course that will be taken to completion. The give & take battle for the past 3-4 years has clearly been in favor of easing and business as usual over addressing structural decay in any meaningful way.
As an analogy, it's like thousands of people crossing a bridge every day for years and an engineering team discovering severe metal fatigue mid-span. Closing the bridge is unthinkable to those using it daily, but only so much repair can be done without a month-long closure. Political leadership can either approve the closure, forcing thousands of people into a forced vacation with many of them likely to go bankrupt because they live paycheck-to-paycheck, or authorize only minor repair that will keep the bridge open while escalating risk that it will fail at a later date.
Likewise, the Fed has been doing patchwork repair for decades when the structural problems needed to be properly handled. The probability of catastrophic failure has been increasing all the while, and now no amount of spit & duct tape will keep things together.
Put another way: if risk of bank failure were increasingly linearly by 1% per year for 99 years and nothing substantial were done to reverse it, there'd be a 100% chance of failure on the 100th year. The real problem is non-linear, and much worse than it seems.