There are some tanks like this, but generally not. Reefs and things like kelp forests are not the same habitat and so for those sorts of algaes it's often a matter of conflicting environmental needs between corals and the algaes. Some macroalgaes are workable in reef tank conditions and they are frequently used as a nutrient sink in sumps and refugiums, but again they are often kept away from contact with the corals to avoid problems (some macroalgaes will grown and/or choke out corals given the opportunity). In one of my tanks I do keep macroalgae in the same tank with corals, but it has to be carefully maintained and I would never recommend it to a beginner.
Seagrasses are another matter. Their collection is prohibited in many places so they are not generally seen in the trade for the hobby. In some places it is legal to collect damaged seagrass that has washed up on shore. I lived in such a place once and tried it - it was extremely hard to get the damaged pieces growing again, and every attempt I made eventually failed even if I had some initial growth. In my case the problem was likely water temperature; my indoor environment kept it too warm even with an unheated tank.
Most corals have symbiotic algae living in their tissues that performs photosynthesis and feeds the coral. For some that's all they need to survive and they will not eat even though they have a mouth and digestive system. Others do better being able to periodically eat in addition to the photosynthesis.