Furthermore, it's often nearly impossible to even be able to ascertain the 'right answer' until you've gained significant exposure to both the application & the business needs; in my experience, you'll have a far better understanding & appreciation of the architecture after a year (or three) of exposure. At that point you are much better positioned to objectively understand the potential ROI (or lack thereof) on a rewrite project vs a more conservative but concerted effort towards incremental improvement over time.
When mentoring developers on this general topic, one of the key things that I emphasize is that a functional application (even if substandard in architecture) is already solving a business need and often generating revenue/profit/positive ROI (as the case may be) for what was probably a "[re]write" project at some point in the past. Rewriting is a large undertaking with many unknowns & high costs, often higher than anticipated, and with no guarantees of reaching full functional parity in a given stated timeline. That results in difficult budgeting & ROI calculations (read: risky), and typically means the project itself is risky -- meaning the potential reward would need to be quite large to be worth it & offset the risks. I find that to rarely be the case when you already have a functional application, even if substandard. ;)