Buffett's criticism is that EBITDA is just accounting and he cares about cash flow, specifically also after paying for CAPEX (which is
Investing Cash Flow so comes after
Operating Cash Flow)
EBITDA is used in the industry because it is a proxy for operating cash flow. Sometimes you don't have all the available data needed to get to OCF, or you're looking at company guidance (for future EBITDA values) or analyst estimates. It's easier to keep the conversation at the EBITDA level because it requires fewer assumptions. Generally the revenue line is ~easy to estimate because you can conceptualize how to go from the current number of customers to some future number of customers, how many dollars per customers and so on and so forth.
Then as you work your way to EBIT (Operating Income) you still have to assume some gross margin, R&D expense, etc. These are pretty tangible. It should be pretty easy to get to estimated EBIT from what the company discloses in guidance or what analysts forecast. Since D&A is pretty linear over time, people generally assume it just remains constant as a % of revenue, so now you have EBITDA which is very much like cash flow
EBITDA is similar to cash flow because it adds back to EBIT the non-cash expense that is D&A. The reason it's good to look at it before interest and taxes is because you're also thinking about how much cash the whole enterprise generates, not how much cash goes to equity holders at the end (which is often called "Free" Cash Flow because it's not tied up with commitments to others)
Coming back to Buffett, in the industries he tends to pick stocks from, CAPEX is a major thing. Companies need to build factories, buy equipment, etc. So if you just look at future EBITDA without accounting for future CAPEX needs, you're fooling yourself.
Truth be told, in those industries everyone also looks at "EBITDA minus Capex". Maybe they do so now that he's bemoaned everyone for not doing it in the first place, but IMHO his criticism largely doesn't apply among valuation professionals. Maybe it does for stock traders, but not for valuation purposes like in an M&A context