If you go back to early versions of Lydiard's books he accepts and encourages participating in races during the base phase. The New Zealand harrier scene that Lydiard's 1950s and 1960s athletes came from had regular cross-country and road races, including road relays. Indeed, that's still how New Zealand running is organized after high school. International athletes were expected to turn out for their club if they could, either to win “inter-club” races, or to support the club through participating, giving the good local athletes a spur to racing better. A lot of these club races would have been handicap races, where the slowest runners start off ahead of the top ones, based on past performances.
However, it's pretty clear that people like Snell and Halberg did not race all out every time they participated in local harrier races. From their times and the description of what else they would do on Saturdays [race day], it seems they treated these races as what we'd now call tempo runs, or what Lydiard called time trials. If you race 5km at your 10km race pace it's a solid effort, but it's not all out racing, and is pretty compatible with training through a race.
I'd really emphasise that in the context Lydiard and his athletes came from, there were some obligations to participate in these races for the sake of the team. Once you had paid your club fees for the year, the races were free. Also for an international athlete like Snell or Halberg, the contrast between the club race and serious competition would have been quite apparent — there's a big difference between an international track meet with thousands of spectators and a club cross country race on a farm in an Auckland park.
That's quite different from the situation many runners in America today face. There's often few, if any, obligations to a team; and a race that costs less than $15 is a bit of a bargain. And the difference between the races we run as workouts and the races we are peaking for are not so obvious. That is to say that there are some good reasons why you shouldn't run races during the base phase if they're really just workouts. You're not obligated to a team to participate, they cost money, and I think you can erode your competitiveness by doing too many races as workouts.
I think if you do too many races as workouts it can become harder to break out of the controlled, holding a little back, mentality that you need for workouts. If you're going to race, race, and go hard. You may be training through it, but that's just something you incorporate into your goals for the race and evaluation of it afterwards. (i.e; if you put in 90% of your peak mileage the week before the race you probably have a good reason for being a little tired). If you're just out there to do something you should be able to do by yourself on a deserted road or track, why do it in a race? Doing it in a workout gives me the extra confidence that this will be easier when there's people to chase and race.
I'd make a couple of exceptions. One is half-marathons at marathon pace, where the opportunity to practice drinking at aid stations and test a marathon-morning routine in an actual race situation can be really valuable. The other is races during the winter where an organized race can sometimes be your only opportunity to run fast on dry roads.
In the end it all comes down to being clear with yourself about what your goals for running are, and how a particular race fits into that picture.