One of the possibilities is precipitation of caco3, when CH is in excess will react carbon dioxide. In later stage it can detiorate the concrete.

To make you understand things in a simple way it would be almost as same as what happens you add fly ash.

And if your intent is to increase strength by adding CH and not affect hydration and setting you need to mix it at the time the cement starts bonding at a molecular level such that when the minute particle starts to separate while we add water, these CH has to be injected to those void spaces. Which would be a highly complicated method to do.

As you mentioned, CH will generally accelerate early hydration and increase early-age strength. But, the 28 d and later age strengths may be adversely influenced. It will depend on the cement chemistry, fineness, and presence of supplementary cementitious materials such as fly ash.

In addition to the given comments above;

The presence of slaked lime will increase the alkalinity of pore solution. The lime saturated alkaline medium can reduce the hydrolysis of unhydrated cement. Thus, early age hydration development of the cement will reduce. The early setting and hardening of cement can be in question thanks to the desication and carbonation of the lime-bearing mix. But there are no these gains at 100% RH because the lime in bulk of the mix cannot be setting and hardening. That is, the early age strength can not be obtained at high-RH environment and if there is no CO2 attack. At later ages, the reduced hydration degree of cement, and soluability and leachability of slaked lime will increase the porosity of the system. Thus, the products will resulted in poor strength and durability characteristics. In addition, the presence of slaked lime can increase the cohesiveness of paste at fresh state, and thus the plastic shrinkage can be in question due to the reduced bleeding capacity. At hardened state, excessive drying and carbonation shrinkage can be observed with loss of water.

if you add CH as chemical additives then C/S ratio is decreased and at lower C/S ratio C-S-H is formed like tobermorite structure with defects. The fraction of such defects meassured by Si NMR. at lower C/S ratio mean chain length increases. The rate of formation of C-S-H is increased and further hydration is depend on the available AL content and gypsum. if the sufficient Al is not available then its later reactivity reduced. Addition of CH increases the rate of reaction in early phase of hydration thus the initial strength gain is higher as compare to Later strength gain.

I think; a low amount of CH can cause an advanced trigger (catalyzer) of cement hydration which promotes the advanced formation of CSH products. Regarding its effect on the structure and performance of the cement matrix; it is enough to add a mineral additive which will fix the excess of CH while avoiding the reactive competition of this addition with the CH of the cement.

Hi

Check the below publication for some very interesting insights on the role of CH on Alite reaction.

Article Micro-reactors to Study Alite Hydration