The biggest problem that design systems solve is connecting the product with the brand and bringing harmony and familiarity to its interface and experience over time. This helps in cultivating product and brand familiarity among its users which can be a very useful asset in the future if you want to launch another product connected with your brand or previous products.
The brand trust and loyalty that your users show in one product will also be translated to the product linked to it if the users recognize the connection. Design systems help you build that connection with design consistency.