Yes, of course buying your own ball joint press will be a more economical way to replace your ball joints, and is doable in an afternoon by yourself. Plus you have the press there the next time you need it for this car or any other job requiring a press.
The point I am making is that it's a hell of a lot of work to take the whole front axle out and take it somewhere to have the ball joints pressed out/in (probably a whole day) when it may only save you $50 over the cost of the press. If you took your whole car and ball joints to a steering/suspension place to install it may take them 2-3hrs tops which would be maybe $150-250. Is your time not worth that?
If money is tight I would be purchasing the press. The less people touching your car, the cheaper it will be and less chance of one of those nasty surprise bills where they say "When we took part X off, we realised part Y was stuffed so we replaced that for you as well". You always have mobile mechanics and/or removing the front axle as a back-up if things happen to go pear-shaped, but provided you follow the YouTube videos and have half an idea when it comes to mechanics I reckon you will be right.
Just my 2c.
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