I'd question your belief that wood could not be precisely fashioned in antiquity. Most of our methods of shaping and finishing wood are exactly the same as those used in antiquity, except that we have machines to do it more efficiently and faster. To fashion a smooth beam or pole all that's really needed is something to smooth the wood--whether sandpaper or polishing stones it does the same job. We have no reason to believe that such shafts would have been any rougher or knottier than any other piece of woodwork, and we know that high-quality pieces of carpentry existed in the ancient world since at least the Bronze Age

There's good reason to believe that early medieval spear shafts were very straight. Wood is rarely very well preserved in archaeological contexts, but we have a few finds of spear shafts from bogs in N. Germany (where wood has a better chance of surviving), and there are lots of tiny fragments of wood preserved inside the sockets of spears from burials in England that tell us a lot of information about how their shafts were made. As a disclaimer, my PhD research specializes on the early medieval English material, so everything I say below has a very England-heavy slant.

In early medieval England, shafts were made in two different ways: from mature timber that was cut down to the right size and shape (this was usually ash), or from sapplings that were already the appropriate size (usually hazel or willow/poplar).

When mature timber was cut to size and shape, it was probably shaved down by hand rather than using a lathe (a long, thin shaft will flex in a lathe; modern walking stick makers who use traditional - ie, 19th century - methods will often still use a variety of hand tools to shape sticks made from timber in preference to lathes). These hand tools give the workman a lot of control over the shape, weight, and balance of the shaft (there's evidence that most early spear shafts tapered along their length), and hand tools allow the maker to follow the grain rather than cutting across it, resulting in a stronger shaft (if you've ever tried to make a spear out of commercial dowel rods or broom handles, which are often cut partly across the grain by machine, you'll know how easily they can shear in half on impact instead of flexing). If the finished, carved shaft wasn't perfectly straight, the maker could gently heat it and bend it straight (a technique still used by modern 'traditional' walking stick makers to straighten shafts).

Shafts made from sapplings could also be straightened and cleaned up very well, if the craftsman wanted to. We have a 3rd century AD shaft from a bog in Vimose that still had bark on it, but a 7th century saint's life (St. Columba) describes a man stripping the bark off a sappling he was making into a spear, using a knife; it's likely that both methods were used. So you might see spear shafts from sapplings with the bark still on, and with small knots and lumps where the branches had been removed. But these irregularities could have been trimmed off with a knife or rasp when the bark was removed (this requires very little skill), resulting in a smooth and regular shaft. Crooked sapplings could be straightened, either by carefully bending them straighter as they dried and cured (a method recommended by some modern walking stick makers), or by heating them over a fire and bending them straight with a simple wooden jig. Here are some modern hazel walking sticks (the group on the left), with the bark left on, that have been straightened with heat - you can see that, despite being sticks cut from a hedgerow, they've been made very straight and regular. And the person who cut them deliberately chose to leave the bark on, and to preserve their primitive stick-like appearance; they could easily be processed further with basic hand tools to smooth out the knots and lumps. So how straight and knot-free these spear shafts were really depended on the preferences of the craftsman rather than the available technology.

So, what were craftsmen's preferences? If you look at late antique art, spear shafts are often decorated with stripes or other regular patterns. We also have carved shafts (with knotwork) from some of the bogs in Iron Age Germany, and a carved shaft (again, with knotwork) was recently discovered in a 7th century AD Anglo-Saxon (English) grave. There's one English case where the excavators recorded some surviving paint on a shaft fragment, but it wasn't chemically analyzed so it remains uncertain whether the identification was correct, or if paint were more common (it probably was). Taken as a whole, although this is really patchy evidence (as is often the case with archaeology, where things only survive by accident), it seems that people did care about how their spear shafts looked and put effort into decorating them carefully. Despite these weapons being generally more utilitarian than, say, swords, a lot of efford went into their manufacture (spearheads, too, show a lot of care to appearance, despite being generally cheaply made). Even rougher spears like the one from Vimose that had bark on its shaft were likely a deliberate form of statement - covered in rough bark, the shaft evoked the wildness of the woods (and the wild beasts that lurked in it) - wild animal imagery was important in early medieval warrior art and poetry. Looking good mattered in early medieval warrior societies, and most of our finds suggest that craftsmen worked hard to ensure that the weapons they produced made the right kind of statement for the warriors who were carrying them.

In the Higgins Armory were quite a number of pikes, halberds, and their variations. Most of them were 16th c., but some were earlier. In any case, a surprising number of them had nails pounded into the shafts, giving them a lumpy-bumpy look. The shafts were, if not original, very very old replacements. This would make some sense, as the normal reaction of a swordsman to a pike would be to chop at it, and nails would make that a bit harder to do effectively. Wood is also a material that can take a lot of nail-driving and still maintain a lot of strength, so it would not have necessarily weakened the shaft much to do this, especially if the nail heads were broad and the nail diameter small.

I would love to refer you to the Higgins website, but it has notoriously closed its doors, and it is hoped the collection will be exhibited at a local museum.