Yes, you can use a 3d Perlin noise field and sample it on the surface of the sphere, to get seamless texture without any anomalies at the poles or projection distortion. That applies to any 3d shape, not just spheres -- it's like carving a solid block of marble. And use 4d Perlin noise to animate it!

It's easy to add any number of dimensions to Perlin noise to control any other parameters (like generating rocks or plants, or modulating biomes and properties like moisture across the surface of the planet, etc).

Each dimension has its own scale, rotation, and intensity (a transform into texture space), and for any dimension you typically combine multiple harmonics and amplitudes of Perlin noise to generate textures with different scales of detail.

The art is picking and tuning those scales and intensities -- you'd want grass density to vary faster than moisture, but larger moist regions to have more grass, dry regions are grassless, etc.