Why can't the distances between our Sun and the celestial objects be measured directly and instead had to rely on looking around for supernova? Is these events frequent, evenly distributed and lasting enough for astronomers to measure any place in our observable universe? Is this method of measurement more preferable than others currently?does this method had any limitations such as an absent of supernova nearby?
Type Ia supernovae are not common; they are quite rare events, happening maybe once per 100-200 years in a big galaxy. Nevertheless they have two properties that make them fantastically useful for distance measurement.
They are (very close to) "standard candles". The physics of the supernova detonation, thought to be when a white dwarf accretes matter and exceeds the Chandrasekhar limit, is very "standardised". The bomb goes off in exactly the same way with the same amount of identical explosive. That means to a good approximation, measuring the apparent brightness of a type Ia supernova and comparing it with nearby examples means that the distances to these events can be accurately estimated.
They are really luminous and last 2-3 weeks. This means that they can be seen at enormous distances, they almost outshine the galaxies that they are in, and they last long enough for astronomers to discover them in automated surveys and still have time to follow them up and measure their light curves and estimate their peak brightness.
The limitations are that you can't choose which galaxies you measure the distance to. You have to wait for a supernova to go off and that might take 100-200 years or more for a particular galaxy. There are also continuing debates about just how standard a candle these objects are. It is possible that more distant galaxies that we see in the very early universe made stars with a different composition (far less elements heavier than helium) and that this alters things a bit. Other problems are associated with "de-reddening" the supernova light curves to account for the possibility of obscuring dust in the host galaxy. It is also possible that there is more than one way to produce a type Ia supernova (accretion of additional mass or merger of two white dwarfs).
I am puzzled by your question "Why can't the distances between our Sun and the celestial objects be measured directly?". Galaxies are much too far away to have a trigonometric parallax distance. Methods like using Cepheids or RR Lyrae variables don't work for very distant galaxies because we can't resolve the individual stars. You could estimate a distance using a measurement of redshift and a cosmological model for the expansion of the Universe, but really the point of using these supernovae was and is to test and improve the cosmological models.