Tillandsia roots are quite different to other plants and are more like a very strong hard wire with a slow setting glue on the end. Once they fix onto a surface, they become like a Boa Constrictor - almost impossible to move. They are so tough, most growers cut them off when they want to move a plant. Likewise old dead roots can also be trimmed off, but make sure not to damage the base of the plant.
Dicotyledons or dicots are flowering plants with an embryo that bears two cotyledons (seed leaves). Dicotyledons constitute the larger of the two great divisions of flowering plants, and typically have broad stalked leaves with net like veins (e.g. daisies, hawthorns, oaks). The roots of these plants tend to continuously fork from the main root into finer and finer roots that take up water, minerals and nutrients. Many of these plants have the ability to produce an acid at the root tip that can help dissolve rock to gain minerals. The fine root hair pushes into a crevice, dissolves a bit more rock and pushes again until it may end up fracturing the rock. There are even cases where these plants have compromised the structural integrity of concrete.
By contrast, Tillandsias are Monocotyledons or monocots which are flowering plants (angio-sperms) whose seeds typically contain only one embryonic leaf, or cotyledon. The roots are more fibrous, do not tend to branch and do not produce a rock dissolving acid. The lack of cambium in the primary root limits its ability to grow sufficiently to fully maintain the plant. This necessitates early development of roots derived from the shoot (adventitious roots). In addition to roots, monocots can develop runners and rhizomes, which are creeping shoots.
Perhaps of all monocots Tillandsias have evolved in a manner where there is little or even no reliance on roots to take up nutrients, this is what holds them apart in the plant world. Compared to monocots, new root growth on a Tillandsia is not massive but any root growth is often a sign that the plant is happy in its environment.
The growing aspect of the wire like roots where the root apical meristem (RAM) is active, is usually a yellow colour and has a succulent look, however, it is quite natural for this to turn brown and look desiccated over time. The plants can produce a flourish of new roots each season, which appears from the hard callused base of the plant. This seems to be a strategy to continually keep pace with the growing weight and mass of the maturing plant to keep it physically secure. In some countries Tillandsias have used these strong roots to anchor on power wires and other structures. T. recurvata is a renowned species for this.
The remarkable thing about Tillandsias roots is that unlike most plants where the roots are buried in the soil, they are fully exposed to sunlight and the air. In fact there are arguments that suggest air movement is also important to their health. Many species can endure the roots exposed to hours of direct hot sulight.
However, some species of Tillandsia that rely on a terrestrial anchor do produce many more roots and can benefit from a loose medium which drains well and an organic root-based fertilizer. There are species which are quite particular about what the root fixes onto while others are extremely tolerant. For instance, I have T. lajensis growing in pots with a loose bark soil mix, on hard rocks, even on clay and others as an epiphytes on trees. While the plants in the mix grow larger, they all grow, flower and produce pups. Despite common perceptions, I have seen Tillandsia roots fix to stainless steel, aluminium, plastic and even treated timber. I am sure in time and the right conditions they could even overtake a slow moving politician.
Interestingly, some Tillandsia roots defy gravity and grow upwards, particularly directly after germination. Maurice Kellett suggested to me it is because in nature the seeds that often germinate and grow successfully are fixed to the bottom of a tree branch - whereas the seed on the top of the branch or rock can get burnt off by too much sun when they are young. So the roots grow upward to get a grip on the bottom side of the branch. Then over time, the plant and or colony grow around and upward to get on top of the branch and then away they go. I have seen T. somnians do this. So there is an advantage in fixing on the underside that give the seedlings an initial radiation protection until they get established.
Also you might like to take a look at the latest version of Tillandsimania which is available at http://lloydgodman.net/Publications/Tillandsimania_Guide_2019_Small.pdf