My guess is that the phenomenon probably makes sense not necessarily in the scope of opioids but in the scope of the neurobiology of addictive drugs. I mean to say that the answer may not necessarily be very closely related to opioid receptors.
In the literature there is a phenomenon known as behavioral sensitization with regards to amphetamines. Whats typically looked at is how fast the animal runs around its cage (locomotion). Its been shown that you can give a mouse a single dose of amphetamine, and even after 1 year of sobriety, it will still display more locomotion than it displayed in its amphetamine naive state.
It seems that with increasing uses of an addictive drug, behavioral sensitization tends to increase. There are neuroplastic changes that seem to be responsible for this and other facets of reinforcement of an addiction, but these addictive drug induced neuroplastic changes can take a bit of time to accrue. Depending on how exactly these changes manifest, it could take time for e.g. proteins to be incorporated into the cell, or something like that.
Then on the 4th day, maybe receptor downregulation starts to kick in and begins to outweigh the neuroplastic changes that enhance sensitivity to rewards.
To put it in more natural terms, the brain's reward/reinforcement systems are supposed to get us to do behavioral things that maximize our likelihood to survive/reproduce, and thus our reward systems are supposed to respond to stuff that actually helps us do that, like food for example. So if we eat a sweet tasting berry in the forest, this kicks in our reinforcement systems, and we are then going to get excited when we see a berry the next day because last time we ate that berry we got (over simplification) a dopamine rush. Then if you eat the berry while excited, maybe it tastes better.
But the neuroplastic changes are what help us feel excited/sensitized, and those may not be as present on day one. Then as the novelty wears off, so will the euphoria, as euphoria is actually very related to novelty oddly enough.
As an example of an alternative explanation, histamine release tends to oppose the desirable effects of opioids, and maybe the first dose does a good job of desensitizing histamine receptors so that the opioids can exert more powerful effects the next day. But this effect doesn't have to be limited to histamine, it could manifest with other neurotransmitters or maybe is better conceptualized as being to do with a neural network as a whole.
There is a "master brake" on the limbic system known as the RMTG, maybe such a braking system needs to be desensitized a little bit on the first day.
Anyone feel free to criticize anything I wrote,
CY