Chemical synthesis takes care of primary structure, but the relatively extreme chemical environment needed typically results in secondary and tertiary structures that do not happen when the macromolecule is synthesized in biological conditions. This is generally due to denaturing (loss of structure). DNA is fairly forgiving when it comes to structure, as nearly all of the information it encodes is in its sequence.

Proteins, on the other hand, use their sequence to create structures to do functions. These structures are relatively delicate and after denaturing are unlikely to return to their original, functional shape. You've experienced this with cooked eggs, where the high heat causes the proteins in the egg to denature and tangle in a way analgous to synthetic condition. "Uncooking" your product as part of its processing is an extremely difficult step that I've never had success with, and generally scales poorly.

There's other factors, like the maturity of the processes (DNA > Protein), the ability to incorporate post-translational modification (DNA > Protein), and the ability to rapidly scale up protein production cheaply via fermentation (DNA > Protein). Once you factor in other concerns, like hazardous materials in synthesis, where you do one hazardous synthesis with DNA before using relatively safe fermentation feedstocks compared to a hazardous synthesis for every milligram of protein you need, it's difficult to justify not just transforming organisms or using a cell-free extract to produce proteins.

That being said, as protein synthesis matures, it may have significant advantages on turnaround time, throughout, and the ability to incorporate non-cannonical amino acids. Currently it can take years to develop strains that can incorporate a single non-cannonical amino acid, and this tech could radically increase the possible sequence space for proteins. It's just not there yet, and it'll likely be a while before we get there. We still have issues with DNA synthesis, and that's a technology that's far ahead of protein synthesis.