Ever since GURPS 4th edition came out, there have been questions about the pricing of ST against Innate Attack. For a basic character, adding +1d punching damage via striking ST costs somewhere between 40 and 50 points, depending on where you are on the ST cost curve. If you add crushing claws (+1 damage per die) and karate@DX+1 (+1 damage per die) you can actually reduce that to 21.5-26.9 points per die, but that's still a long ways away from an innate melee (C,1) crushing attack costing 4 points per die.
In the end, I think this is because in games where people use innate attack, it was expected that you wouldn't be balancing punching people with ST -- you'd be balancing people using their ST to pick up a hyperdense vibroblade (+4 striking ST will give +1d(10) Cut, Melee C,1, Device(breakable, can be stolen); 17.5 points) and maybe buffing it with Power Attack and Weapon Master, at which point ST actually looks pretty reasonable. Unfortunately, there exist large genres where powers exist, and yet the primary use for ST appears to be punching people, not necessarily even with fancy martial arts moves.
If you want a 100% rules-legal method of dealing with this problem, that isn't intended to only work at cosmic power levels (super-effort works fine if you're interested in doing hundreds to thousands of dice), there actually is one: alternate attacks. Rather than buying ST +4 [40], buy striking ST +4[20], Lifting ST +4[12], HP +4[8], and then buy Innate Attack +5d Crushing, Melee (C,1), Alternate Attack (of Striking ST) [4]. This has a lot of advantages in terms of flexibility, since you can define just how you want your super ST to work (for example, double knockback would be very appropriate to some genres). Unfortunately, this can wind up being either peculiarly limited or forcing you to buy a large number of extremely similar powers -- if you want to be able to throw both cars and motorcycles at people you need to have two different powers, since they have different levels of area effect. Still, something resembling this mechanic does have an appeal. Therefore, we're now going to sidestep to another topic.
Fundamentally, the effect of ST is to increase the damage of other abilities, that you either have natively, or that you acquire through some means, such as weapons. You can think of +8 Striking ST (on a ST 10 character) as:
+2d damage to all attacks with the properties ST-based and Swing.
+1d damage to all attacks with the properties ST-based and Thrust.
Written this way, it looks like an advantage, not an attribute. The question, then, is: "What is the proper value of the +1d advantage?" Unfortunately, the only really plausible answer is "That depends on the power and variety of attacks it modifies". To take a degenerate case, something that boosts a single attack is presumably worth the same as a single die of that attack, and there's no easy way to come up with a fair price for something that might boost an attack costing 2 points per die, or an attack that costs 50 points per die. Unless... we make the effect of the boosting power vary with the cost of the power being boosted. Consider this power:
Boost Damage: 5p/level
Allows you to increase the damage of your attacks. With no limitations, applies to any attack you make. To determine the increase in damage, divide your levels by the cost of a level of the attack being boosted (for example, it takes five levels of boost to add 1d to a crushing attack). When computing the cost of a die of an attack that you did not purchase as an innate attack (for example, boosting the damage of a gun), all limitations should be ignored -- i.e. if you boost the damage of a sword, you ignore the fact that it's a device that can be damaged or stolen, and has reach 1. The ST-based advantage should also be ignored. Boost is usually limited to only apply to a subset of attacks.
This looks pretty reasonable; it's a clear relative to powers like modular abilities, and there's no way you can use it to make an attack be cheaper than its normal cost, since even a limitation of -80% would leave a cost of 1 per level. This gives us a very simple way of handling super-ST: replacing Striking ST with Boost Damage (ST-based attacks only). That's a fairly large limitation, as it leaves out an awful lot of quite useful weapons; in a modern game it's plausibly worth -40 to -50%. We'll go with -40%, for a convenient cost of 3/level. Almost every attack you're going to be boosting will be a non-advantaged crushing attack, so every 5 levels of this advantage (costing 15 points) will give us a die of damage.