Don't they always stay inside the autonomous region due to organiser/sponsorship reasons?
If they won't use roads in Navarra, they're probably not likely to cross the French border either.
If Sicard had developed into a worldbeater, it might have been a different story.
Itzulia uses Navarra all the time though?
I mean, Lodosa hosted the ITT in 2018, Pamplona hosted the first stage in 2017, Lesaka in 2016, Urdazubi/Urdax in 2014, Ibardin in 2012, Lekunberri in 2011, Viana in 2010, Villatuerta in 2009... and the Urdax and Ibardin stages also crossed the border into Iparralde.
Most likely is that the issue in the three Iparraldean provinces the most money is in Lapurdi/Labourd, the coastal area, including Hendaia, St-Jean-de-Luz, Biarritz, Anglet and Bayonne (the latter at least historically). These are perhaps parcours-wise less interesting and in Bayonne and Biarritz the big sporting interest is rugby, even if Biarritz Olympique are going through tough times at the moment, a far cry from their glory days of Imanol Harinordoquy as captain and taking on the best in the world representing the Basque country by
wearing a giant ikurrina. French Basque identity is often less strong than in northwestern Navarre and in Euskadi proper, which also plays a role. There is a bit more Basque identity in the smaller towns and more isolated provinces, but realistically then it would need the capitals of the inland Iparraldean provinces, Saint-Jean-Piéd-de-Port (Basse-Navarre) or Mauléon-Licharre (Zuberoa) to pay for the race to come to town, and they are somewhat further afield. Hendaia also crops up as an almost everpresent host of the Vuelta al Bidasoa, an important amateur race in the Basque borderlands.