We can find some hints in scripture.
Fifth part as a general rule of compensation for trespass
First, the requirement of adding a fifth part is not just about "holy things" but is the general requirement for making amends as part of a trespass offering:
Numbers 5:6–7 (KJV 1900)
Speak unto the children of Israel, When a man or woman shall commit
any sin that men commit, to do a trespass against the LORD, and that
person be guilty; Then they shall confess their sin which they have
done: and he shall recompense his trespass with the principal thereof,
and add unto it the fifth part thereof, and give it unto him against
whom he hath trespassed.
Leviticus 6:1–5 (KJV 1900)
And the LORD spake unto Moses, saying,
If a soul sin, and commit a
trespass against the LORD, and lie unto his neighbour in that which
was delivered him to keep, or in fellowship, or in a thing taken away
by violence, or hath deceived his neighbour; Or have found that
which was lost, and lieth concerning it, and sweareth falsely; in any
of all these that a man doeth, sinning therein:
Then it shall be,
because he hath sinned, and is guilty, that he shall restore that
which he took violently away, or the thing which he hath deceitfully
gotten, or that which was delivered him to keep, or the lost thing
which he found, Or all that about which he hath sworn falsely;
shall even restore it in the principal, and shall add the fifth part
more thereto, and give it unto him to whom it appertaineth, in the day
of his trespass offering.
The extra 20% has to be given to the one who was cheated.
Therefore it makes sense that if one takes from the holy things, that a fifth part has to be given to the priest (Lev 5.16, Lev 22.14)
Note that there is a duality (both linguistic and symbolic) between "fifth" and "five". E.g. When the Philistines want to make a trespass offering for stealing the ark:
1 Samuel 6:4 (KJV 1900)
Then said they, What shall be the trespass offering which we shall
return to him? They answered, Five golden emerods, and five golden
mice, according to the number of the lords of the Philistines: for one
plague was on you all, and on your lords.
Five is the same root as fifth ch-m-sh.
Fifth part as the redemption fee
Anytime something (or someone) is vowed to the Lord, it can be redeemed by paying the value plus a fifth. This applies to all things and people except those "devoted" to the Lord, who cannot be redeemed for the 20% fee and must be put to death. This includes offering land to God and then taking it back. See Leviticus 27.13, 27.15, 27.19, 27.27, 27.31. Even tithes and first fruits can be redeemed for an extra 20%.
This makes the 20% penalty a generic redemption penalty. We can view the eating of the consecrated bread as special case since it was devoted to the Lord but the congregation used it. So the congregation owes 20% and obviously the person who did the eating should be the one to pay the redemption fee.
Contrast with grace
From this we can get at least a hint as to why 20% is required, in that it is dual to 5, the number of grace. Grace is an unearned gift, whereas the redemption fee is a paid price -- the opposite of grace. It is also the root for fat and stomach.
Joseph gave the Egyptians an impossible burden -- they would have 20% (chimesh) of their labor confiscated by Pharoah and then would need to buy it back in order fill their bellies (chamash) during the lean years. The amount the Egyptians paid is the redemption price: 120% of their income, since 20% was taken from them and they had to buy it back.
This creates a crushing debt that is impossible to pay, since the redemption price is designed so that you cannot pay it for yourself, as it's set at 120% of your life earnings (see table in Leviticus 17 of various redemption prices for different people based on age and sex).
As the Egyptians struggled to pay this impossible debt, they sold all their possessions, all their land, and eventually became slaves of Pharaoh on Joseph's instructions.
But for Benjamin, whom Joseph favored, he gave him a five times (chamash) portion of food (Gen 43.34) - this was completely unearned, but the result of favor, and thus grace. He gave all his brothers a coat, but for Benjamin, five coats (Gen 45.22). Again, an unearned abundance.
Thus the world is divided into those who are from Egypt and so struggle to pay their own redemption price - a debt that they cannot possibly pay -- and those who get five times unearned blessings as a result of grace. Who are the recipients of grace? Those who come out of the same womb as Joseph, e.g. those who are born from above. Everyone else must slave as they try to redeem themselves.