The concept of work engagement (Schaufeli et al., 2002) is not flawed.
However, recent research — which unfortunately for this site, is in German — shows that more research about the predictors of work engagement is needed.
Höge and Schnell (2012) demonstrate that meaning in work (or: meaningful work) can fully mediate the relation between core job dimensions (e. g. predictor variables like task autonomy or task identity) as defined by Hackman & Oldham (1975) and the criterion variable work engagement (Schaufeli et al., 2002). In other words: Perceiving one's work as meaningful is an important but not well known antecedent of work engagement.
Hackman, J. R., & Oldham, G. R. (1975). Development of the Job Diagnostic Survey. Journal of Applied Psychology, 60(2), 159–170.
Höge, T., & Schnell, T. (2012). Kein Arbeitsengagement ohne Sinnerfüllung.: Eine Studie zum Zusammenhang von Work Engagement, Sinnerfüllung und Tätigkeitsmerkmalen. Wirtschaftspsychologie, (1), 91–99.
Schaufeli, W., Salanova, M., González-romá, V., & Bakker, A. (2002). The Measurement of Engagement and Burnout: A Two Sample Confirmatory Factor Analytic Approach. Journal of Happiness Studies, 3(1), 71–92. https://doi.org/10.1023/A:1015630930326
For those wanting to learn more about meaning in work there is an English-language paper which is, however, not related to work engagement:
Schnell, T., Höge, T., & Pollet, E. (2013). Predicting meaning in work: Theory, data, implications. The Journal of Positive Psychology, 8(6), 543–554. https://doi.org/10.1080/17439760.2013.830763