I don't think the numbers given in your example are particularly realistic. Series A rounds are almost never smaller than seed rounds and are usually at least 3x - 10x.
If you raise $2m or $3m on uncapped, no-discount notes, you basically need to turn that into a $10m+ pre-money company upon raising your Series A. If you raise $4m or 5m+ seed, it gets even harder. And this is assuming no cap or discount, which is unlikely.
You are correct that Series A rounds are usually not smaller, in which case if you raise several million seed on uncapped notes and cannot leverage that into a much more valuable company, you'll be unable to raise a Series A.
This is all manageable by the entrepreneur, but it's important to make sure you understand what's happening and where the risks are. It seems a lot of entrepreneurs don't.
There is no "rule" about implied valuation either. Entrepreneurs can raise $3m in notes $100k at a time, usually from investors that are much less price-sensitive than VCs leading a priced round. It's a lot harder to raise a priced Series A at a $10m+ valuation than raising piecemeal notes at the same valuation cap (or uncapped notes, even).
Again, this is all manageable by the entrepreneur, but there are no "rules" like it often appears from the outside.