Mexico did develop a thriving olive oil industry. Olive cultivation was introduced by Franciscan and Jesuit missionaries very soon after the Spanish conquest - some trees planted in 1524 near Mexico City are still producing olives. From Mexico, the olive travelled to Peru in 1560, and California in the 18th century [1]. At least, that's the Mexican version of the history - the Argentine claim is that the olive arrived in Argentina in 1556, then went to Peru in 1560, and continued on, reaching Mexico in 1697 [2]. (Similar claims - both ways - appear in historical notes in oil industry journals and publications [1,2], and historical introductions in technical works focussing on olives and olive oil [3] (which don't tend to be very reliably written history, since they're written by scientists in a hurry).)
The problem was that the industry was too successful. In the 18th century, Mexico was self-sufficient, and exporting to other Spanish colonies [1]. This was illegal - Spain had already banned inter-colonial trade in goods that were important Spanish exports (olive oil, wine, and more) in the early 17th century. In 1774,Carlos III of Spain banned further planting of olives in Mexico, and in 1777 ordered all olives trees except those on Church land to be destroyed [1]. Spain's economic attitude to its colonies was one of exploitation, not cooperation [4,5,6]. So Mexico went back to being an olive oil importer in the late 18th century. This left lard and beef tallow as the easily available cheap fats, and these became dominant [6]. Grape cultivation and wine consumption followed a similar pattern.
Tapas is fairly straightforward: it only became a big thing in Spain after Mexican independence. While there are various stories about the Medieval origin of tapas, it's more likely to have developed in the 19th century [7]. It's a dining style for the urban and affluent. While there is a very old tradition of street food in Mexico (pre-Columbian [8]), which continues, the traditional focus was a cheap meal - fast food rather than social dining. The growth in restaurant culture in Mexico is relatively recent (late 20th century), and even now such dining is too expensive for many [8]. Even if tapas was old enough, it would have been something for the elite.
Jamón ibérico I can't say much about. One contributor to its lack might have been the popularity of beef during the heyday of the Mexican cattle industry (to a large extent, a leather industry aiming to export and producing beef (and tallow) as a cheap by-product for the domestic market) [6].
References:
Emerson, L. P. Bill (1980), Mexico's expanding olive industry, Washington, D.C.: U.S. Dept. of Agriculture, Foreign Agricultural Service https://archive.org/details/mexicosexpanding294emer
Navarro, J., De Canales, G., and Patac de las Travieras, L. (1961), "La Olivicultura en la Republica Argentina", Boletin de Oleicoltura Internacional 64-65, 17-23.
Giorgio Bartolini, Raffaella Petruccelli (2002), Classification, Origin, Diffusion and History of the Olive, Food and Agriculture Organization of the United Nations
Kathleen Deagan, (2003), "Colonial Origins and Colonial Transformations in Spanish America", Hist Arch 37: 3. https://doi.org/10.1007/BF03376619
Thomas Grennes, (2007), "The Columbian Exchange and the Reversal of Fortune", Cato J. 27, 91
Super, J., & Vargas, L. (2000). Mexico and Highland Central America. In K. Kiple & K. Ornelas (Eds.), The Cambridge World History of Food (pp. 1248-1254). Cambridge: Cambridge University Press. doi:10.1017/CHOL9780521402156.016
Ruiz de Lera, Enrique (2012), "Gastronomy as a key factor in branding Spain", chapter 7, pp. 115-122 in OECD Studies on Tourism Food and the Tourism Experience: The OECD-Korea Workshop, OECD.
Janet Long-Solís and Luis Alberto Vargas (2005), Food culture in Mexico, Greenwood Press.