I have been looking at examples of large solid fuel rocket boosters or first stages used for space launch, such as P80, the Space Shuttle SRB, the various versions of Graphite-Epoxy-Motor, the solid fuel booster for Ariane 5 or the first stages in the Minotaur family. It seems that (max thrust)/(weight full of fuel) is typically in the range of 2-3, and I can't find any reaching a thrust/weight of 4 or higher. With the specific impulse of these rocket motors, this corresponds to a burn time in the order of 2 minutes.
In contrast, artillery rockets, and air-to-air and surface-surface to air missiles often burn out in a few seconds, reaching an acceleration of tens of G's. However, these are much smaller, and tend to have a smaller propellant fraction than those used for space launces.
High initial acceleration can limit gravity losses, admittedly at the cost of higher dynamic pressure, but still I would have thought it is beneficial to get higher thrust out of these rocket engines , particularly the side strap boosters.
Now the question: Is there some practical limitation to thrust to weight when solid fueled rockets become larger, or is the higher thrust simply not that useful?