One vaccine isn't enough to provide protection. When you give a single vaccine that required within a series, it only produced a small antibody spike. You want a large body reaction to the given vaccine.
This chart shows you how the body creates antibodies after a vaccine is given. IgM and IgG are antibodies that the body produced in a response to a threat. There are 5 classes of antibodies. You can see a small consistent jump in the IgM after the Primary vaccine and booster vaccine have been given (5 weeks apart in this particular chart, which is not specific to any vaccine.) IgG is the most common AB (antibody) produced in the body and you can see it's small increase in productivity after the primary vaccine. Then it decreases after weeks...so if you don't do the booster vaccines, the first vaccines become null and void. This small "blip" of IgG after the first vaccine is not powerful enough to fight an infection if the puppy is exposed before the vaccination schedule is finished. That "blip" of antibody production grows with each vaccine. When it gets to a certain level, (after all 3 vaccines) then the body is ready to protect the puppy from that particular threat.
Vaccines differ: Lyme vaccine requires a booster after only 2 weeks, because it's antibody productivity decreases faster than those in a 4 in 1. Bordetella requires only 1 vaccination for the body to be adequately protected from kennel cough for a year.
The antibodies themselves will always decrease after a vaccine is given, so the IgG isn't going to say consistently high after all 3 shots are given.
The real goal of a vaccine is to produce Memory cells, which are another type of B cell (which all these listed antibodies are also B cells....ah, How I miss immunology class!) Memory cells are what stay in the body long-term (for years, or sometimes a lifetime). When a virus or bacteria is introduced to a body that has been exposed to the same virus or bacteria before (in a vaccine), the Memory cells are what jump into action, they produce the antibodies that are required to fight off that sickness...so you'll get that spike in IgG or IgM again, but this time, instead of being produced as a reaction to a vaccination, they are being produced by these Memory cells and to a reaction that's the real thing. "This is not a drill!"
When you booster a vaccine every year, (or every 10 years for a tetanus vaccine in a human, for example), you're keeping a fresh supply of memory cells in the body that are ready to respond to a problem quickly and effectively.