You can make such variance seem a lot less punative if you tie good and bad things to it. This is another trick that I picked up from Burning Wheel which happens to make changing the time required for rests more interesting. The BW version isn't tied to healing, though the applications to D&D healing I think are obvious. (BW injuries are serious things that put you out of commission for weeks, months, or even years--a different tone entirely.)
In BW, you have a "resource" stat that largely substitutes for managing wealth. Each resource period, each character must check against resources to maintain their lifestyle--failure generally costing them resources and success maintaining or even gaining. A great haul of treasure gives you a handful of one-time bonuses to such rolls. The group can set the resource cycle period however they want for that campaign. Test every week, and you are playing a heavy social/mercantile game. Set it once a year, and you can ignore for stretches at a time. Most games will set it for a month or a season. But note what happens here. A resource cycle is a chance to gain, to apply that treasure, to advance in the world. It's also a chance to get the moneylenders clamoring for your head, for the baron to demand service, etc. So the length of the period is "how often do we want to deal with this stuff, positive and negative alike?"
With short and extended rests, you can get some of that same feeling by making the rests have costs besides simply using time. This can be simple and abstract costs (pay so much per month for basic food and upkeep) or can be as elaborate as the group wants to detail--buying every last medicinal brandy by the silver piece.
The trick to making this work, however, is that if you set "extended rest" at "once per day", then you pay the cost every day, whether you needed the rest to get back wounds and spells or not. Suddenly, you might see some interest in setting to "week" or "adventure" or whatever fits the tone of the game. Or alternately, if the group still wants once per day, perhaps they like the challenge of gaining enough gold to maintain that rapid pace.