ROA as a Proxy for WACC

I was thinking about the previous brilliant question asked at the Rotman Stock Pitch and I wanted to extend the idea a bit further. While I know there are some obvious short comings in the analysis (and idea of proxies) I would like to make the following proposal:

ROA is a proxy for WACC

Most people know that ROA has to be greater than WACC in order to be profitable. Also, the accounting in the proof highlights an idea I've been struggling with:

A as a proxy for D + E VERSUS L + E

First WACC is calculated as:

WACC = ke (E / (D+E)) + kd (1-t) (D / (D+E))

= [ke * E + kd (1-t) * D] / (D+E)

And ROA is defined as:

ROA = [NI + Int Exp (1-t)] / A

However, recall that ROE is a proxy for ke so:

WACC = [ROE * E + kd (1-t) *D] / (D + E)

Note that ROE * E = NI and
kd * D = Int Exp

Therefore (with some assumptions and proxies):

WACC = NI + Int Exp (1-t) / (D+E)

So we can see that WACC is strikingly similar to ROA. What's the difference? This is the original problem I was having before.

The difference between WACC and ROA is that WACC has a denominator of (D+E) whereas ROA has a denominator of A.

What's the difference? A is L + E, not technically D+E. So what's the difference between Liabilities (L) and Debt (D)?

Debt is technically only Long term debt + Short Term debt (and perhaps minus cash, depending on the financial model?)

L is ALL the liabilities, including Current Liabilities (CL) and "Other long term liabilities".