The Death of Ivan Ilyich uses a third person omniscient narration, so the narrator is able to describe the thoughts, actions, and motives of multiple characters. If the first four chapters of the novella were told from Praskovya Fyodorovna's point of view, her judgment and perspective would have clouded the way we see the thoughts, actions, and motives of the other characters. For example, if the section about Ivan Ilyich's funeral had been told from her perspective, the narration might have been overly focused on her apparent grief. But readers, privy to her internal thoughts, would also realize that she didn’t care much about her husband, in life or in death. She might have centered the narration around Ivan Ilyich's suffering, how even she suffered because of Ivan Ilyich's illness, and how it was better now that he was gone. She would describe the ordeal she went through in the last few days before Ivan Ilyich's death. Given her apparent selfish character, she might well have made it seem like she suffered more than Ivan himself.
The account of their marriage would also have been different if told from Praskovya Fyodorovna's perspective. She would probably portray Ivan Ilyich as a suitable match for herself. She might focus on the fact that he was a successful magistrate from a good family with good character and fine dancing skills. She would describe their courtship, how she fell in love with him, and their marriage in greater detail. She might tell us how she was really happy to be married to him, at least initially, and describe the first few months of her marriage as beautiful and happy. She’d likely describe how being a mother was hard and demanding, made more difficult by a husband who wasn't supportive. She would describe her outrage when Ivan starts to spend more time with friends, at parties, and at bridge games, apparently to avoid her.
Her perspective about Ivan Ilyich's illness would also be very different from what we actually read in chapter 4 of the novella. She'd probably complain about how Ivan was trying to get attention by fussing about some trivial health problem. She'd feel that his illness was his fault because he wouldn’t follow the doctor's instructions and would eat and drink all the wrong things, while she had to bear the consequences of his "illness."
Some details from the first four chapters would also be missing if the story were told from Praskovya Fyodorovna's point of view. For example, we wouldn’t have known of Ivan Ilyich's colleagues' thoughts about and reactions to his death. Praskovya wasn't part of this discussion, and she obviously couldn’t read their minds. She wouldn't have been able to write about Peter Ivanovich's fears and thoughts about death. The details of Ivan Ilyich's early life would also vary depending on her knowledge of Ivan Ilyich's family and his childhood. She wouldn't have been able to describe what Ivan was going through after their marriage and the birth of their children because he wasn't sharing his thoughts and feelings with her. And lastly, she was probably clueless about Ivan Ilyich's health concerns and his fear of death because they didn't talk much about it.