Despite the critics' barbs, canine-themed token Dogecoin (DOGE -1.92%) has come a long way over the past couple of years. Once a joke token, Dogecoin is now among the most popular digital assets, with a market capitalization in the billions of dollars.

Yet the always-enticing $1 threshold remains elusive. Sure, the recent broad-based cryptocurrency bear market could be partially to blame. After all, like in the world of stocks, a strong inter-asset correlation means that a falling crypto tide will sink all (or at least most) boats.

Nonetheless, the dream of Dogecoin clearing the $1 bar makes the token enticing for crypto-market speculators of all stripes. However, while Dogecoin has at least one famous fan/fanatic, the burden of proof still rests squarely on the bulls' shoulders, as reputational issues are tough to shake.

Possible vs. probable

Can Dogecoin reach $1? Of course, it can, but sensible investing revolves not around what's possible but what's likely to happen. Unless you're buying a handful of Dogecoins just as a throwaway lottery ticket, the point is to assess whether the coin has a fair shot at hitting $1 within a reasonable time frame.

Based on the math alone, $1 may be further away than you think. Sure, Dogecoin touched $0.73 briefly on May 6, 2021, but that was during the peak of meme-trade mania. For a hot minute, it was "cool" for regular folks to send Gamestop and AMC stocks, and even silver, "to the moon". Surely it's not a coincidence that Dogecoin's rocket ride and subsequent decline coincided with the rise and fall of the meme craze.

Now that the novelty of the meme trade has worn off, investors shouldn't count on retail renegades pushing Dogecoin back toward $1. If they didn't succeed then, they wouldn't likely get another crack at it, especially with Dogecoin recently trading for less than a dime.

Powerful, but not all-powerful

If you had to name ten famous Dogecoin supporters, that might be a tall order. Yet naming one of them is easy as Tesla (TSLA -1.53%) CEO and sometimes-world's-richest-person Elon Musk has been quite vocal in his support of Dogecoin. He's even gone so far as to announce that "Tesla will make some merch buyable with Doge & see how it goes," a disclosure that caused Dogecoin to pop to $0.20.

That rally didn't stick, though, and neither did the Dogecoin spike that followed Musk's announcement that "soon SpaceX merch too" could be purchased with the token.  Musk's influence over individual crypto coins' price movements only runs so deep and so far, evidently.

Besides, Musk can't single-handedly fix the reputational issues dogging Dogecoin nowadays. First of all, Musk is being sued for $258 billion over a claim that he's been involved "in a crypto pyramid scheme by way of dogecoin cryptocurrency."  Even if that gets resolved one way or another, Dogecoin seems to have even more disturbing connotations. While concrete proof may be hard to come by, analytics firm Elliptic claims to have "identified millions of dollars worth of Dogecoin transactions connected to illicit activity," while pinpointing Dogecoin-funded activity "including terrorism financing and vendors of child sexual abuse material."

Without delving into the sordid details of these alleged illicit connections, it's at least safe to say that there's still a lingering, unsavory Wild West element to the world of altcoins. Whether claims of nefarious activity involving Dogecoin can be substantiated or not isn't the point -- either way, mega-corporations and the public may be hard-pressed to accept and adopt Dogecoin for the foreseeable future comfortably. Amid that challenging backdrop, and with or without Musk's backing, getting Dogecoin to $1 will be doggone near impossible.