Besides the answer by TheChymera, there's also the "problem" that interstitial fluid can't really flow freely.
Blood runs in veins, allowing to quickly circulate through your entire body. And if you cut yourself (and cut one or more veins), there is a direct path for the blood to take.
Interstitial fluid, however, has to creep through all kinds of small openings, not having a free path. Compare driving on the highway (crowded though it might be) and crawling through houses in a crowded city. Sure, if you're an experienced parkour-athlete you can get through. But if everyone wants to get out of a city, getting out over the highway will be the fastest.
By the way, there is one situation where you may "bleed" interstitial fluid: in a blister.
Here, the waterproof (and interstitial-fluid-proof) part of your skin detaches, and the fluid can accumulate. But it will do so only slowly, creeping through some small openings.
And the fact that it comes in slowly is also what makes a blister a problem, as it also means it can't flow back quickly. So if you press on it, it feels like some trapped fluid, even though you could in principle keep on applying pressure and push it back.