lagrangian formalism - Constraints in classical mechanics

I am self-studying classical mechanics and I have a couple of questions about constraints. Goldstein in his book Classical Mechanics writes in the beginning of Section 1.3 that:

It is an overly simplified view to think that all problems in mechanics are reduced to solving the set of differential equations: $$m_i \ddot{\bf r}_i ~=~ {\bf F}_i^{(e)} + \sum_j {\bf F}_{ji} \tag{$\dagger$}$$ where ${\bf F}_i^{(e)}$ denotes the net external force on particle $i$ and ${\bf F}_{ji}$ denotes the force exerted by particle $j$ on $i$ because one may need to take into account the necessary constraints for the system.

Then, he says that the constraints introduce two types of difficulties in solving mechanical problems:

$(\text{I})$ $r_i$ are no longer independent.

$(\text{II})$ constraint forces are not known in general.

My questions are:

$(1)$ IF it is possible to identify all the constraint forces, then all the problems would be reduced to solving $(\dagger)$, where ${\bf F}_i^{(e)}$ includes all the constraints forces. Wouldn't it? If not, is there a constraint that cannot be translated into a corresponding constraint force?

$(2)$ Isn't $(\text{II})$ in fact the only difficulty with solving mechanical problems? It seems to me that $(\text{I})$ is not a "difficulty" because provided we can identify all the constraint forces the fact that $r_i$ are not independent would be incorporated into the constraint forces that would appear in the equations of motion. Isn't the fact that $r_i$ are not independent nothing but that the equations of motion are coupled ODEs?