Having an "arcane skill" be an Attribute instead of a Skill is a bit unusual and something that neither the core rules, nor any supplementary setting that I am aware of, has ever tried to do. I think that you hit on one of the biggest consequences:
Why would anyone not take Arcane Background (Psionics)?
This is the biggest issue I see. Why would anyone not take Arcane Background (Psionics)? They could take an Edge like Alertness, giving them +2 to Notice checks, or they could take a single Edge and be able to cast 3 powers (including offensive powers, like bolt). While some players might want to not be Psionic for story reasons, I can't think of a reason that a player interested in making the most powerful character would choose not to take this Edge.
What's the point of increasing Fighting, Shooting, or Throwing?
Another issue I see is that there really isn't any point in taking conventional weapons. A character with the Arcane Background (Psionics) Edge can take an offensive power, like bolt, and deal damage. If they have average Smarts, they roll it at a d6.
Most Arcane Backgrounds have a skill to provide a tradeoff. You are good at Fighting or Shooting or Psionics, but generally not all of them. In core Savage Worlds, this tradeoff means that a character has to decide if they want to specialize in psionics or something else. As it stands, there is no tradeoff here, at least among skills.
You may argue that the Power Points would encourage characters to diversify. I think that in practice, players will just take the New Power Edge to overcome this issue. A starting HUman character with 4 Hindrance Points can take the Arcane Background (Psionics) and the Power Points Edge twice, starting with 20 Power Points, and then can gain another 5 each rank. If they have Edges like Soul Drain or Power Surge, they are unlikely to ever run out.
It's easier to get better at Psionics
Say that we are using the Psionics skill. A character might have a d6 Psionics and a d6 Smarts. If the character wants to raise it to a d8 Smarts, they have a choice. They can either spend 2 skill points and raise it (because it is above the linked Attribute), or they can increase Smarts to a d8, and then next Advance increase Psionics by 1 skill point (and use that other skill point somewhere else).
With your method, there is no opportunity cost. With a single Advance, you can increase a characters Smarts, and their psionic ability at the same time. Increasing Smarts has other benefits, like making it cheaper to buy Smarts skills, improving Common Knowledge rolls, and making it easier to deal with Smarts Tricks and Taunt Tests of Will.
Anybody, psionic or not, can make a Cooperative psionic roll
Cooperative rolls are permitted if a character is trained in a skill. Attribute cooperative rolls (e.g. Strength cooperative rolls) are always permitted because a character cannot be untrained. This would mean that anybody can assist in a roll to help a caster, with or without the Arcane Background. Now you could add a rule that only those with the Arcane Background can make a cooperative roll, but I think that this is another reason to wonder why anyone would not take Arcane Background (Psionics).
Competent psionics will be more common than you intend
Another note: Good, experienced psionics are really rare and mostly work for the church, but mediocre psionics and especially those with just "a bit" of power are quite common.
As it stands, anybody with Arcane Background (Psionics) and a character with d6 Smarts (average for a Human) will be able to cast their powers about 50% of the time (an average roll on an exploding d6 is 4.2). If they are a Wild Card, that number is even more likely. This doesn't seem to mesh with your idea of those with just "a bit" of power being quite common, as it would mean that those who are of average intelligence are pretty competent psionicists.
If instead you used the Psionics skill, then having Psionics who are untrained or have a d4 Psionics would be easier to justify as having mediocre or "a bit" of power.
What does this fix over the core rules?
The core rules contain a version of Arcane Background (Psionics) that is so far identical to what you have, except that it uses Smarts instead of Psionics. Why was this change made? By understanding the rationale, you may be able to find alternative solutions that aren't so much balance breaking.
What alternatives might there be?
Let's say that your intention was to make it so that those with psionic ability can tap into power with little only a little training. I think we've established that having this happen all the time is a bit game breaking compared to those who don't have it. So maybe this is something they can do some of the time but not all of the time.
In that case, you could add a rule to Arcane Background (Psionics) that the character can spend a Benny in order to use their Smarts instead of their Psionics for a limited amount of time (either one time, for a number of rounds, or for the duration of the scene). Thematically, a psionic character "taps in" to their ability. By spending a Benny, there is a cost associated with it, meaning that they will be less likely to reroll and soak, while those who are not psionic will have more Bennies to do that. This will better balance those who are psionc with those who are not.