What place do solid rocket fuels have in spaceflight?

[Jim]

Likely the use of solids is mostly because big ICBM makers had control over rocket designs.

nope, that is not the reason.

[Jim]

, and the Delta III had nine strap-on solid fuel rocket boosters because the greater payload mass of the Delta III to LEO and GTO compared to that of the Delta II necessitated the provision for a large number of SRBs to provide enough initial thrust for the Delta III.

Stop posting misinformation.  Do research and composition without using AI.   
Delta I/II used 9 solids for more than 200 of its launches.

[Jim]

I don’t understand. I can see why people use solid Rocket motors for kick stages, but for any other application I don’t think they have a proper place in spaceflight.

wrong, they have a place just as much as cold gas thrusters, hypergolic propellants, LH2, H202, etc have a place.

[Vahe231991]

, and the Delta III had nine strap-on solid fuel rocket boosters because the greater payload mass of the Delta III to LEO and GTO compared to that of the Delta II necessitated the provision for a large number of SRBs to provide enough initial thrust for the Delta III.

Stop posting misinformation.  Do research and composition without using AI.   
Delta I/II used 9 solids for more than 200 of its launches.

What was rationale for various numbers of Castor solid-fuel boosters being used on numerous pre-Delta II variants of the Delta rocket, namely the Delta 0100, Delta 1000, Delta 2000, and Delta 3000, even though multiple Castor SRBs offered added thrust for the Delta 0100, Delta 1000, Delta 2000, Delta 3000, and Delta II upon liftoff?

[edkyle99]

What was rationale for various numbers of Castor solid-fuel boosters being used on numerous pre-Delta II variants of the Delta rocket, namely the Delta 0100, Delta 1000, Delta 2000, and Delta 3000, even though multiple Castor SRBs offered added thrust for the Delta 0100, Delta 1000, Delta 2000, Delta 3000, and Delta II upon liftoff?

The launchers were tailored to their missions.  Payload mass and orbit determined the number of solids.  Only three solids were used at first.  Six and nine-solid variants arrived later.  RCA paid for development of the more powerful Castor 4 solid in order to launch its Satcom series to GTO, creating the Delta 3914 variant.  Meanwhile, NASA was still flying relatively light NOAA satellites to sun synchronous orbits, requiring only a Delta 2310.  Etc.

 - Ed Kyle

[Jim]

What was rationale for various numbers of Castor solid-fuel boosters being used on numerous pre-Delta II variants of the Delta rocket, namely the Delta 0100, Delta 1000, Delta 2000, and Delta 3000, even though multiple Castor SRBs offered added thrust for the Delta 0100, Delta 1000, Delta 2000, Delta 3000, and Delta II upon liftoff?

STOP USING AI.  Your own post answers your question.

What was The rationale for various numbers of Castor solid-fuel boosters being used on numerous pre-Delta II variants of the Delta rocket , namely the Delta 0100, Delta 1000, Delta 2000, and Delta 3000, even though multiple Castor SRBs offered   is added thrust.  for the Delta 0100, Delta 1000, Delta 2000, Delta 3000, and Delta II upon liftoff?