You can’t make a blanket statement about the grape without qualifying it.
When made well, there is no grape capable of making wines that live longer. Some, like Nebbiolo, can live as long. Many years ago I was able to taste a lot of old wines fairly regularly and I realized that once you hit say, thirty years or so, the ones I liked the most were always Tempranillo based. So I started drinking those. If you like older wines, some can definitely improve with aging.
But not all.
The wine you tasted is from a bodega in Rioja that dates back to the late 1800s. In the 1900s, those wineries tended to make wines with extended cask aging and additional bottle aging. The classifications of crianza, reserva, and gran reserva designate aging requirements, but most of the wines were aged far beyond the minimum aging requirements. And most were also aged in American oak. But not necessarily brand new 225 liter oak barrels. There is no requirement regarding the age or size of the barrels in Rioja.
Back in the early days the wines would often have a bit of Cabernet, Mazuelo, Graciano and Garnacha. And sometimes a bit of Viura, a white grape. Over the years they decided not to use Cabernet any more. What people typically call “traditional” is based on rules dating to the 1970s.
And then in the 1990s, everything changed. People started using new barrels frequently, sometimes made from oak from different European countries, they aged the wines for shorter periods, picked grapes riper, cleaned up their bodegas, and basically modernized.
So today you have a wide variety of approaches, depending on the wine maker and the specific wine he or she is trying to make.
As for tannins, Tempranillo almost never has harsh tannins, at least when made well. Remember it’s made in other regions too. Probably the most tannic is the Tempranillo from Toro, far more than that from Rioja. The key in Toro is to tame the tannins and not pick too late. Very few people have mastered it to the point that they’re making wines of elegance as opposed to power. Same in Portugal, but there Tempranillo is usually not the dominant grape. In Ribera del Duero, the wines tend to be somewhat between Rioja and Toro, which makes sense as the location is between them. The Tempranillo from elsewhere is generally from warmer places and you’re not likely to find a lot of it in the US, other than perhaps from Navarra.
In the US, there’s no really great Tempranillo made yet, at least as far as I’ve found. I think it’s only a matter of time, but I taste as many as possible and none are yet on the level as some of the basic Spanish ones. That includes rather expensive versions from producers like Cayuse and Abacela.
The wines of Rioja Alta will always and forever have a bit of oak that’s very detectable. Or at least for sixty five years, which is the oldest I’ve had from that bodega.
So depending on the location and the producer, the grape can age more than just about any other grape. But sometimes it’s no good after a year. Inevitably, someone will announce that you should drink wines from Lopez de Heredia. You shouldn’t unless you like their specific style. I think most people haven’t had a lot of Spanish wine in general so they try what others on this board suggest. But there are many producers worth exploring.
BTW - I’d be interested in knowing which were harsh and tannic.