I have seen traditional marline sold by chandleries catering to the more hard-core, uncompromising, traditional sort of sailors. Otherwise often referred to a 'pigheaded fools'. The romantic sort who still dream of 'wooden ships and iron men', rolling seas and eschew many of the benefits of modern chemistry.
Nothing quite has the same aesthetic sense and wholesomeness of a traditional wooden boat with bronze fittings subtly scented by the smell of marine tar, teak and salt spray.
But your right. Many of the traditional materials do have serious problems. Most of the stuff sold as 'tarred marline' is actually tarred brown Dacron. This is mainly what you get if you buy marline from most chandleries like Defender:
http://www.defender.com/product.jsp?path=-1|118|311417|311408&id=21227
It isn't as aesthetically pleasing but it comes in a color and form that look a lot like the traditional stuff but it doesn't degrade much in sunlight or rot.
The old-time stuff is still sold:
http://www.tarsmell.com/marline.html Ttraditionally it was sold in balls by the diameter and pound weight. It comes in various thicknesses. The thinner stuff can be used for stitching, finishing the ends of ropes and light lashings while the thicker is better for heavy-duty lashings like you might need to keep that 200 pound anchor secured when the boat capsizes.
They also sell "Stockholm tar" in case you wish to tar your own line. Or just like the smell.
http://www.tarsmell.com/tar.htmlThis stuff has a lot of uses. A dab on a tool handle will give you a good grip. Rubbed into wood and it will resist water, rot and insects. Applied to cloth and you have the basics of traditional oil cloth that is somewhere between water repellent and waterproof depending on how tight the cloth is and how much tar, and the specific mix, you use. Everyone has their own 'dope'. usually a mix of pine oil, wax, and enough solvent to make application easy. Wrap your tools in oil cloth and they resist rust.