Having investigated the use of OpenStreetMap data in the past year, I have to say that it's still disappointing and not complete enough to be used as a serious solution.

If I look at university nodes that have a website in France I find 241 unique values which represents less than 10% of the total amount.

Are you sure there are more than 2410 universities in France? Running the SPARQL query below at https://query.wikidata.org/#SELECT%20%28count%28DISTINCT%20%... , I get 218 French universities with a Wikidata item (which usually means there's a corresponding Wikipedia article) but for "higher education institution" I get 675: https://query.wikidata.org/#SELECT%20%28count%28DISTINCT%20%...

Query:

  SELECT (count(DISTINCT ?school) AS ?count)
  WHERE
  {
    # find instances of subclasses of university Q3918 (use Q38723 for higher education institution)
    ?school wdt:P31/wdt:P279* wd:Q3918 .

    # in France
    ?school wdt:P17 wd:Q142 .
  }

Typically, there is no perfect data source and their applicability depends on your use cases. OpenStreetMap is first about streets, then (geometries of) buildings, POIs etc. An attribute like website information has not been high on the use cases that the community has but I think this is getting better with more use and especially the integration with Wikidata.

In Wikidata, I can currently get 563 results for institutes of higher education in France with website information: https://query.wikidata.org/#SELECT%20DISTINCT%20%3Fschool%20...

EDIT: Applied the fix by yorwba to get more results.

You need to add an asterisk after wdt:P279, otherwise the query only finds instances of direct subclasses of Q38723. On the other hand, I didn't think to filter only for those that have an associated website. (See sibling comment.)

Modifying your query, I get 563 results: https://query.wikidata.org/#SELECT%20DISTINCT%20%3Fschool%20...

Conclusion: it depends on how you count.

Thanks for noticing and fixing my bug!

The chicken and egg problem is that OSM will be as good as the data it gets, and the data it gets will increase as people use it as a serious solution and contribute where they find it inadequate.

Sure, but companies have the money to contribute a subscription but not time, because the later is incredibly more expensive for them.

This makes OSM data a non-starter in most serious business use cases.

It varies a lot by location. Some places are kept up to date by contributors and some aren't.