intuitive interpretation of the marginal return/productivity of capital being less than one
Several thoughts in this area:

1) Capital stock lasts over time. I may trade 1 euro for 1 unit of capital. This capital returns 0.01 euros every period forever.  It pays itself off eventually. 

2) If one has an incredible high rate of return and a sufficiently low discount rate, one might have divergent consumption paths, ex: I spend all of my money on capital, each unit of capital returns \$2 for the next period. I repeat forever, but never consume anything, because any consumption represents a loss of \$2 tomorrow.  After 1000 periods, I have a huge amount of capital but no consumption.

3) Cobb-Douglass is normalized so the exponents sum to one. This led to some off-the-cuff work. It has derivatives: 

$MPK =\alpha_k * (\frac{L}{K})^{1-\alpha_k}=\alpha_k k^{-(1-\alpha_k)}$

$MPL= (1-\alpha_k) (\frac{K}{L})^{\alpha_k} = (1-\alpha_k) k^{\alpha_k}$ 

In optimal long-run state, these two will be equal. 

$\alpha_k k^{-(1-\alpha_k)} = (1-\alpha_k) k^{\alpha_k}$

$\alpha_k = (1-\alpha_k) k^{\alpha_k --(1-\alpha_k)}$

$\alpha_k = (1-\alpha_k) k^{1}$

$k^{1} =  \frac{\alpha_k}{1-\alpha_k}$

Plug this back in and you get:

$MPL^{*} = \alpha_k \frac{\alpha_k}{1-\alpha_k}^{-(1-\alpha_k)}$

$MPL^{*} = \alpha_k \frac{\alpha_k}{1-\alpha_k}^{\alpha_k-1}$

$MPL^{*} = \alpha_k \frac{1-\alpha_k}{\alpha_k} * \frac{\alpha_k}{1-\alpha_k}^{\alpha_k}$

$MPL^{*} = (1-\alpha_k) * \frac{\alpha_k}{1-\alpha_k}^{\alpha_k}$

$MPL^{*} = (1-\alpha_k) * \frac{\alpha_k^{\alpha_k}}{(1-\alpha_k)^{\alpha_k}}$

$MPL^{*} = \frac{\alpha_k^{\alpha_k}}{(1-\alpha_k)^{\alpha_k - 1}}$

$MPL^{*} = \alpha_k^{\alpha_k}*(1-\alpha_k)^{1-\alpha_k}$

This looks like it's some sort of fraction. A quick screenshot on wolfram alpha suggests indeed that is the case.