Is it possible to buy all the skills?

As killing enemies earns experience points, which eventually lead to a level up and a skill point reward, it is a safe bet that you can earn enough skill points to buy all the available skills in the game, by killing enemies and completing quests.

This is reported on the Twinfinite site also.

it looks like the max level cap is level 50. By this point, you’ll have already earned enough skill points to unlock all of the available Skills.

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Upon reaching level 50, you’ll also earn a bronze trophy. It’s the final level-related trophy, so it’s a good sign that this is the max level cap in the game.

Ref: twinfinite.net Max level cap

The top row of skills all cost 1 skill point, the whole row costs 9 points. The second row skills cost 2 points, with a total of 18, and the last two rows of skills all cost 3 points each, totalling 54 point for both rows.

So in all you'll need to earn 81 skill points to buy all the skills. Might be 80 in total, as I think Silent Strike is given for free.

As mentioned by @Shaz in the comments, there is also a trophy for unlocking all the skills.

Yes, it is possible to unlock all the skills; here is the proof:

This is with the Frozen Wilds expansion pack included¹ but not played through².

To get it I:

1. levelled up to the maximum (level 60).
2. played all quests and side quests of Horizon Zero Dawn (excluding Frozen Wilds). This includes all the Hunting Grounds missions getting all Blazing Saddles Suns.
3. got all the collectables³. You get skill points when you sell Banuk Figures, Metal Flowers and Ancient Vessels.

Additional note: when I had one skill (costing three skill points) to "buy", I had seven skill points. When I bought it, I "lost" those four extra skill points.

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_{1 I have the Complete Edition.}

_{2 That is, I have played through the entire Horizon Zero Dawn main campaign but none of Frozen Wilds.}

_{3 Training Dummies only add a badge, no skill points.}