The wrap and compression stocking over that act to compress the treated vein to prevent blood from pooling in the treated vein. If blood accumulates in a treated vein, it can cause increased tenderness and can lead to hemosiderin staining of the skin. If stains occur, they will often fade or even disappear but that can take up to a year. I advise using the wrap as your doctor suggest to prevent problems down the road
Varicose veins and venous insufficiency are chronic conditions. The treatments that we do have high success rates but you have millions of veins in your legs and other veins can go bad in the future. I do phlebectomies through needle holes (no incisions) and most patients are back to work the following day and occasionally patients will go to work right after the procedure. In my experience people feel better after vein treatments and are happy they had them done.
EVLT and RFA are pretty much equivalent. I myself prefer RF but honestly they both do a good job. Phlebectomy is also great for treating large superficial tributary varicosities but in the right hand and right setting ultrasound guided sclero can have great results too. I use both techniques in my practice and tailor the treatment to the patients anatomy and preferences. The long term success rate for an ablation should be over 95%. Having said that, 25 procedures seems very excessive. I do feel that venous insufficiency is a chronic disease and you very well may need more treatments later in life. I always encourage people to get second opinions if they are not comfortable with recommended procedures. A vascular surgeon should know how to properly treat veins but ask what percent of their practice is spent on treating veins vs arteries. Some vascular surgeons spend the vast majority of their practice treating arteries and only dabble in vein care and thus may not be as up to date as someone who only treats veins.
The vein pictured is a reticular vein. These veins run just under the skin and can often "feed" spider veins. It can be treated with cosmetic sclerotherapy or even a very limited microphlebectomy if you do not like the appearance but it is not a clinical concern and does not need to be treated, especially if you are not symptomatic.
Everything in life has risks, including doing nothing. Chronic Venous Insufficiency and varicose veins cause many more cases of secondary lymphedema than the treatments of these conditions. While there are risks with treatment, they are very rare, especially in experienced hands.