What recruiter told you that you didn't get a job because you did a modular ATPL instead of an integrated one. That is preposterous!
Eh? When you can't put in an application to an airline because low hours jobs are not even advertised, you kind of don't need to be told by a recruiter "We don't hire modular types!" - It's blindingly obvious.
Let's look deeper: EasyJet only hires low houred pilots through CTC. BA and BA Citiflyer only from Oxford, CTC and possibly FTE. FlyBe (mostly speaking) also from the big schools and the top 3 providers of low hours pilots into Ryanair are the standard big integrated schools too. Go into Europe, and it's the same situation across France and Germany. Spain, I'm not sure?
But they're not the only airlines in Europe you say? True. But for those there is competition, fierce competition especially if you have zero commercial experience or no type rating. And skill has very little to do with it. More so than skill, luck and being at the right time/place is what brings successes. You are competing with thousands just to get a phone call or invite.
I think we are living in alternate realities my friend. From what I've seen (also been flying privately since my teens), the FI route into commercial flying has become less viable as the years have passed. The 3 FIs who I know (some who are also experienced examiners) all in their 30s who are getting jet jobs right now have over 3,000 instructional hours and had to SSTR + P2F to get ahead. A few success stories doesn't change the overall situation. I believe I have the bigger picture covered in my analysis.
That "demand" you talk about is just an excuse you use to feel better.
I don't need to feel better. It was and remains an accepted bitter choice. I'm not unique in this department. I've come across many who feel the same. For me, it was this way or the highway. In life, we need to do what works for us, given our own personal situation. Your reality is not the only one a pilot can experience.