A typical classroom ball on a string demonstration of conservation of angular momentum starts at 2 rps and has the radius reduced to ten percent.
$$L_2=L_1$$ $$L=mvr$$ $$m_2v_2r_2=m_1v_1r_1$$ $$m_2=m_1$$ $$v_2r_2=v_1r_1$$ $$\text {divide both sides by } r_1^2r_2^2$$ $$\frac{v_2}{r_2r_1^2}=\frac{v_1}{r_1r_2^2}$$ $$\omega=\frac{v}{r}$$ $$\omega_2=\left(\frac{r_1}{r_2}\right)^2\omega_1$$ $$\omega_2=\left(\frac{10}{1}\right)^2\times2rps=200rps$$ Convert to revolutions per minute $$\omega_2=200\times60=12000rpm$$ Roughly the rotational speed of a formula one race car engine on full throttle at full speed.
This is very obviously wrong and it is unreasonable to claim that roughly a ten thousand percent loss of energy can occur within the second that it takes to pull in the string.
You don't need to go through all those equations, you can just start with $L = I\omega$ then substitute $I = mr^2$. Since angular momentum is conserved, reducing $r$ to $0.1r$ would indeed increase $\omega$ by $100$ times.
So your result is correct, and your intuition is the one that's wrong.
Energy is not conserved* because you need to do work to pull the ball in. $E = \frac{1}{2} I \omega^2 = \frac{1}{2} m r^2\omega^2$. Since $r$ decreased to $0.1r$ but $\omega$ increased by a factor of $100$, the new fast-spinning ball has $100$ times more energy, and you will need to do work to pull the ball in. Note the new system has more energy, not less. It's part of the reason why [it's hard for a stellar system to collapse][1].
*More accurately, energy is conserved, because the amount of energy gained by the system is exactly equal to the amount of energy needed to pull the ball; in. The latter can be calculated from $dW = F \cdot dS$, where $F = -mr\omega^2$ is the centripetal force.
The integral equation you need is
$W = \int_r^{0.1r} mr * \frac{L^2}{m^2r^4} dr = 49.5 \frac{L^2}{m r^2} = 49.5 m r^2 \omega^2$
Meanwhile the energy of the system increased by $99 \times \frac{1}{2}I\omega^2 = 49.5 mr^2\omega^2$, exactly equal to the work you did against the centripetal force.