All round parachutes have many suspension lines, and they're needed to distribute the load on the canopy, keep its shape, and their hooking (or even re-hooking) geometry during deployment can help with reefing and keeping its shape. It's not because we can't make suspension lines strong enough. Fewer suspension lines would require stronger canopy that would then likely result in even heavier parachute, and fewer sections would result in less controlled reefing and it would be more prone to collapsing and canopy tearing.
Soyuz TMA main parachute is a rather large annular pull down apex type that deploys after the spacecraft has already decelerated to subsonic speed with the help of two pilot and four drogue parachutes 15 minutes before landing
 that reduce the rate of descent to ~ 80 m/s (288 km/h)
 before the main parachute deploys, and it has a small apex hole to increase stability and reduce oscillation. From that linked Wikipedia page:
A variation on the round parachute is the pull down apex parachute.
Invented by a Frenchman named Pierre-Marcel Lemoigne it is called a
Para-Commander canopy in some circles, after the first model of the
type. It is a round parachute, but with suspension lines to the canopy
apex that apply load there and pull the apex closer to the load,
distorting the round shape into a somewhat flattened or lenticular
Some designs have the fabric removed from the apex to open a hole
through which air can exit, giving the canopy an annular geometry.
They also have decreased horizontal drag due to their flatter shape
and, when combined with rear-facing vents, can have considerable
So, while all those suspension lines do add to parachute's weight, and there's another point you missed in your question that a large parachute is even more difficult to fold properly (terribly important with parachutes!), if it used fewer suspension lines, it would have fewer sections that would somehow have to be even stronger then. And it would have problems keeping its shape once deployed because of larger sections, and due to this more prone to instabilities or tearing of the canopy.
So even if we could construct a chute with stronger suspension lines and canopy fabric, we likely wouldn't use any fewer suspension lines. As for entanglement of suspension lines, well there's always a chance you'll be having a really bad day, but that risk is reduced by using a single main parachute and pilot chutes that pull it out and help it reef. If lines entangle, there's still a good chance that the canopy will be able to keep its shape, lines will only stretch out (hook) from a bit higher up. Compare that with usually three main parachutes that most other spacecraft use, and you start appreciating that it's a tradeoff, and no solution is bulletproof.
Using many main parachutes means they can get entangled, canopies can bump with each other and partially or fully collapse, and there's even more suspension lines, but you can still get home for dinner if only one of them fails. With a single one, if that one fails, you have to deploy the spare one
 and there might not be any time for that. It's a calculated risk and a design choice. But there isn't much point in reducing the number of suspension lines and parachute sections.
- NASA - Soyuz Landing
- RuSpace - Soyuz landing profile
- ESA - Soyuz TMA (PDF)