Do you need an Alpha Aniimo for a strong build?

What an Alpha saves you is the work, not the ceiling. One caught in the overworld already has the enhanced version of its Core Skill, so it never needs a pact with its Held Item to unlock it. Take the long route and you catch an early evolution, evolve it yourself, then spend shards to link the item. You end up in the same place, just with fewer resources left over.

So a strong build never depends on finding the Alpha. If a species' Alpha is awkward to reach, the evolve and link route gets you a full build. You just pay for it in shards.

Are Alpha Aniimo better, or just cheaper?

Not every Alpha is a good one. They vary in quality when captured, so one with poor stats can still lose to a well-rolled creature you evolved yourself. Because quality varies, you can farm Alphas for better stats, and that is where the real advantage comes from if you are willing to repeat the fight.

Captured area bosses, Stellarys among them, are Alpha-sized, so the same reasoning covers them. An Alpha is also not a dead end. You can convert one into its Prismana form later with a Prismana Orb.

When fighting the Alpha pays off anyway

Some evolutions require you to beat a specific Alpha. Defeating it satisfies that requirement and awards its Alpha evolution stones even if the capture fails, and catching it counts as well. Defeating each Alpha for the first time, Alpha Minespine included, also awards an Irisalis petal without consuming energy. So even if you plan to evolve rather than catch, the fight is often worth taking.