Allow me to explain why the iceburst series is perfect the way it is, and a fantastic weapon. :)

First of all, let me ask you just what good it would do you to have a small, random chance of freezing things with each attack when you're using a three-hit combo? Because, yes, if it was going to happen on the regular hits it would be at a much less frequent rate than we get when it's only on the charge, for balance purposes. You'd be freezing monsters and then immediately unfreezing them. When you really really NEED them to be frozen, it probably wouldn't happen, or at least not as soon as you want it to happen. You'd either be chopping away at monsters, unfreezing them as soon as you freeze them or putting yourself at risk of counter-attack while you wait for the freezing to happen. Or you could just smack things once and then shield, and then smack them once more and then shield... but then it would still take too long and you wouldn't be doing a lot of damage in the meantime. Furthermore, again because of balance issues, if they were going to make it have a chance to happen on every attack they'd probably lower the strength down from Strong, which is absolutely no good if you're actually trying to use freeze for crowd control. If you're only trying to use freeze to keep them still long enough to get behind them and make your next attack, then... well you'd be putting yourself at risk getting that close to them and wasting a lot of time, just for the sake of getting one easy hit in? Totally defeats the purpose, especially with the higher-tiers of the series, where the charge attack explosions can reach farther and thus freeze monsters from an increasingly safer distance away. The basic attacks on the other hand are as short reaching on the glacius as they are on the 3* iceburst brandish.

With a hail driver, you're freezing the monster from outside it's attacking range. You can freeze it up WITHOUT putting yourself in danger and THEN go in for the easy hit, or use it to help yourself escape because you can move away from the monsters WHILE you try and freeze them instead of having to get CLOSE to them. With the hail driver you also have less chance to accidentally un-freeze a monster as soon as you freeze it because typically you're putting more time between each shot than between attacks in the sword's combo. I'm assuming that you've actually been using the freezing alchemer series since you referenced it, and therefore you know that the only time you fire both shots at once is when you absolutely have to do double the damage right away, and otherwise you space them out a little so that you don't have to reload.

Another reason you really really would not want the basic attacks of the iceburst series to freeze is because sometimes you do NOT want to freeze a monster. What if your teammate has just melted an entire room-full of ice jellies with a fire haze bomb? If you attack them with a weapon with a chance to freeze, you risk... err... freezing them! In a more general note, freeze also cancels out fire status. If your teammate has lit up all of the monsters in the room and they're taking some really heavy DoT, you could extinguish the flames with one attack. Or say you want to push a monster? They don't move if the attack freezes them.

That is the beauty of the iceburst series. It reliably freezes monsters as soon as you want it to (well, a couple seconds later) and it never freezes them when you don't want it to. You can slash away at burning monsters and melted jellies, and you can crowd-control half-a-room-full of monsters in a single attack. On top of that... the damage is actually pretty good for such a fast series of weapons.

If you really want to use it to its absolute best effectiveness, try this: Charge attack as many monsters in a group as you can. Most of them will now be frozen. Back off and sidestep a little so that you can start pounding the ones that didn't freeze without accidentally hitting and unfreezing the others. About the time you finish killing the non-freezers, the ice will wear off, and because it was STRONG freeze, it will do about as much damage to them as -the initial charge attack itself did-. They'll either die from it, or be nearly dead at this point, and either way.. they were out of your hair while you had an effortless fight against the couple that escaped.

On a side note, some of this holds true for the fireburst series as well. Obvious, a chance to burn on every attack would be a lot more useful than a chance to freeze on every attack, but for BALANCE reasons a weapon that can do that (like the Flamberge series) is going to do it a lot less reliably and with much weaker fire status than what you get with the fireburst series, where you simply open up the fight by inflicting strong fire on most of the monsters and then either backing up to charge up the next hit for the ones that didn't burn, or start doing your basic combo on the ones that are already on fire.