First off: I assure you all the instruments used for the International Chopin Competition on Period Instruments are in top condition. Many of them are modern copies anyway so those didn’t go through 150 years of wear and tear, and they would only use originals they could restore to their prime.
Why there is a little more reverb is a result of long and complicated history which I will summarise in very general and imprecise terms (you have been warned).
Before the beginning of the 20th century, piano design was not standardised at all so every builder more or less did their own thing. Fortunately, we can distinguish some major traditions/schools of piano building.
The first one of importance to this issue is the 18th century Viennese tradition (I know, you asked about the 19th century). Of course, at all points in history instruments and music are tightly related. (Very) broadly speaking, 18th century Viennese music emulates human speech, so pianos from that time and region are very well-suited to producing clear, transparent and well-articulated sounds (so they have excellent dampers, for example).
At the end of the 18th century, a different school emerged: the London pianos with most notably Broadwood’s piano factory. The London instruments went for a bigger sound with more resonance, so they have terrible dampers (don’t get me wrong, this is by design; I just mean that they are not very effective at their only task: damping).
During the first decades of the nineteenth century the London pianos start to go out of fashion and Paris becomes a new piano centre. The two big names are Pleyel and Erard, makers of most instruments used in the ICCPI.
Both of them are somewhere in between the Viennese and London style, with Erard being closer to London and Pleyel being closer to Vienna. Chopin preferred Pleyel, Liszt preferred Erard (as did surprisingly many ICCPI competitors, but maybe the Pleyel they used was not loud enough to fill the big halls - let’s not forget they were meant for salons, mostly).
The fact that the dampers in your grandmother’s upright didn’t work so well anymore, however, is because of a lack of maintenance (unless you are in your 80s and your grandmother inherited it from her parents, who got it when they were young). From about 1850 onwards we have quite good dampers, steadily improving.