In 2016, the EU published a report on the TPD and why it had never been activated so far. The main work on the paper was done before the 2015 "refugee crisis", so it contains no conclusion from that episode, especially from the influx of Syrian refugees.
The first observation about the directive is its inprecise language (p. 17).
In sum, the broad – or vague – use and definition of the term ‘mass influx’ in the Directive was to allow for the possible activation of the TPD in the context of different types of mass influx. However, in the absence of definitions of these different types of mass influx, and indicators on how to measure these, stakeholders agree that it has been hardly possible to attain Member State agreement on the (possible) activation of the TPD.
The second observation criticises the activation process as "cumbersome" (p. 19):
Should the TPD be activated in the future, this may potentially undermine its very objectives, i.e. to rapidly relieve the pressure on national asylum systems affected by a mass influx of applicants for international protection and to provide immediate access to those applicants (in clear need of international protection).
...it was noted that the activation process can only be initiated by the
Commission, either ex officio or upon request of a Member State. The Member State’s request only has to be examined, it does not oblige the Commission to submit a proposal to the Council to activate the mechanism. Article 5 (2) of the Directive describes in detail the content of the Commission’s competence to such a proposal. Once the Commission has submitted its proposal, the Council can adopt a Decision to activate the temporary protection mechanism by qualified majority.
A third observation notes that since 2001, a large amount of other legislation has been adopted by the EU to handle mass influx of migrants (p. 30):
...since 2001, several Member States’ asylum systems have significantly evolved, including a surge in and subsequent consolidation of experience and knowhow on how to deal with situations of pressure. Moreover, at EU level, the legal and political context in the field of asylum has significantly changed...including also the tools available at EU level that aim to assist Member States in handling large influxes.
...In response to the situations of pressure as experienced in 2001-2014, preference was given to alternative measures both by the Commission as well as Member States...
But the core of the failure of the directive was the missing solidarity mechanism. Articles 25 and 26 talk about "a spirit of Community solidarity" and urges "the Member States shall cooperate with each other", but there is no further implementation for these intentions. Thus the paper concludes (p.24):
...the expectation that Member States indicate capacity is problematic without common criteria to calculate or project reception capacity. This may not only lead to Member States declaring that they are unable to receive beneficiaries, but also to disagreement between Member States and disputes within the Council as to the factual – but also ideal – capacity of each Member State. This slows down, but may also compromise, the prospect of an equitable burden-sharing.
A 2019 study by H. Deniz Genç and N. Aslı Şırın Öner notes there were at least three occasions where an activation could have been reasonable, but did not happen (p. 7f):
After the 2011 Arab spring, Italy and Malta encountered large numbers of refugees arriving across the Mediteranean. Both countries requested the activation, but it was turned down by the Commission on grounds of the numbers not being high enough.
The start of the conflict in Ukraine in 2014 brought a large influx of refugees to Poland, but Poland did not experience an excess pressure on its asylum system and thus saw no reason to ask for the activation. The EU report (p. 138ff) explains that most refugees used Poland only as a transit point. In 2015, about three quarters of them withdrew from the asylum procedure there, and traveled on to other destinations (p. 28).
After Syrian refugees started to arrive in large numbers on the Balkan route, it were "academics, activists and social workers that called for an activation". The European Left GUE/NGL brought a resolution to the European Parliament, but the text adopted no longer mentioned the directive. No member state requested the activation, as required by the directive.
Instead, the member states discussed the ammendment of the Dublin III treaty with a "crisis relocation mechanism". The failure to find a consensus led to a new emphasis on deterring refugees from entering the EU and the EU-Turkey refugee return agreement.