So my dummy load resonates?

It does if the reactance is zero - that is the definition of resonance.
If you are measuring one end of a coax cable, and the SWR is 1.0 : 1, you don't know whether there is
an antenna, a dummy load, or the input circuit to an amplifier (or an infinite length of coax) at the
other end by a single measurement of impedance. The load still looks like 50+j0 to the transmitter -
are you saying that in some cases that is a resonant impedance and sometimes it isn't?
And, like W6RMK, returning to the original post, if the question is whether you NEED an SWR analyzer
to tune up antennas, the answer clearly is no. You can do it with an SWR meter: tuning the antenna
for minimum SWR is at least as good as anything else for this purpose.
Beyond that there are two arguments for the SWR analyzer: it is portable, and it gives some indication
of resistance and/or reactance beyond just SWR. These need to be considered separately.
Portability is good: I remember lugging my HW-12 and 45 pound power supply (pair of 866 rectifiers)
up onto the roof as a kid to tune my 80m antenna. Years later the Ten-Tec Argonaut with a built-in
SWR meter made life much simpler. I've also used the remote key lead technique when I needed to
adjust a variable capacitor at the external tuner: I left the radio in the shack but put the SWR meter
at the antenna and used a long wire to key the transmitter as needed. (The conventional approach
was to have a friend come over and key the transmitter while you adjusted the antenna.) You can
even build your own simple crystal-controlled oscillators with SWR bridges if you are interested in
a limited number of frequencies. While there are ways around it, portability is the biggest argument
for some sort of SWR analyzer in my mind. That's what I use my MFJ-209 for (though sometimes
I still take a radio out into the back yard so I can make QSOs on the antenna.)
Measuring resistance and reactance can be useful, but it certainly isn't essential for building antennas.
I've built and experimenting with LOTS of antennas over the years, and can think of one time that I
needed to measure the R and X (to make a matching stub to use a 155 MHz on 2m.) In that case
I built a simple circuit that reads out impedance on the face of an oscilloscope. Otherwise I've
managed fine with SWR (which is all I get from my MFJ-209). Is the antenna too short or too long?
measure the SWR at several points and find out - this is much more accurate than checking the
reactance though an unknown length of coax. Is the resistance above or below 50 ohms? Put a
200 ohm resistor across the feedpoint and see if the SWR gets better or worse. Need to measure
a complex impedance? Build an experimental "L" network and adjust it to get a match, then measure
the values of the components. Need to cut a quarter wave stub? Connect a resistor of the desired
impedance across the far end, or put it on a T connector with a dummy load and short the far end,
and adjust the length for minimum SWR.
Not that having R and X might not make things easier sometimes. If I had such an analyzer I'd certainly
use it, but the point is that you can do a lot without it. In fact, sometimes it provides TOO MUCH
information, and the operator loses track of what really matters. The crowd that insists on X=0 (though
a random length of coax, when that doesn't necessarily coincide with minimum SWR) are one example.
I've also seen folks totally mess up tuning a gamma match by basing their adjustments on the frequency
of minimum SWR rather than the SWR at the desired frequency.
I guess what it boils down to is that the knowledge of what you are doing is more important than how
fancy your test equipment is. If you can't afford a fancy analyzer, don't let that stop you from
experimenting with antennas. You may need to learn a bit more about impedances and SWR to know
how to interpret the readings, but that is a useful thing to do anyway. As you get more experience
with antennas, you'll find some places where an SWR analyzer would be more convenient, and you may
decide that is worthwhile for you to acquire one (or find a friend you can borrow from.) If I didn't
have the MFJ-209 I probably would have bought a fancier one by now, but so far I don't seen enough
added benefit to upgrade.