Should 屋 and 居 use radical 户 instead of 尸? 户 means home. So these examples are not suprising: 房 fáng (house),  扁 biǎn (flat), 扇 shàn (fan [mostly used indoor]), 扉 fēi (door)

尸 means corpse, and it looks like it refers to tail or something leaving downwards, so these examples are not suprising either:
尿 niào (urine), 尾 wěi (tail), 屎 shǐ (poo), 屁 pì (fart)

However, 屋 wū (room) and 居 jū (live) under 尸 is suprising since it seems to belong more to 户 by its meaning.

Is this discrepancy above due to a calligraphical mistake or lazyness, namely, leaving off that one tick, made a long time ago?

sources:

http://justlearnchinese.com/chinese-radical-show-home-radical-42/

http://justlearnchinese.com/chinese-radical-show-corpse-radical-41/
Is this discrepancy above due to a calligraphical mistake or lazyness, namely, leaving off that one tick, made a long time ago?

TL;DR: I don't think so, because (1) 尸 used as the pictographic radical with the meaning house in 屋 was explicitly mentioned in 说文解字 long before, (2) the original meanings of 尸 and 户 used as radicals are not exactly the same (house vs single door).
1. About 尸 (and 屋)
尸 used as the pictograph in 屋 was explicitly mentioned in 说文解字:

居也。从尸。尸，所主也。一曰尸，象屋形。(尸 looks like house.)
会意。从尸,从至。尸,与房屋有关,“至”表示来到。人来到这里居住之意。

This article summarized three usages of 尸 when used as radical.
(italics is translation from me)

A.从原意而来，代表人的躯体。(Derived from the original meaning, represents body of human.)
会意字有：
屍：死去的躯体，就是尸体。屍和尸古来就一直通用。
尿：躯体排出的水分。
屎：米经过躯体排出来的东西。
屄：躯干上的洞。
尾：躯干后面的毛。
等等。

形声字有：
尻，屌，屈，屑，屙，屁
属（声旁是蜀，不是禹），
届（声旁是凷，不是由），含义是到达，比如届时，无远弗届等等。
展，屠，
尼：原意为靠近，后来用昵字代替了本意。至于尼姑的尼，则是梵语比丘尼（bhikṣunī）的音译缩略。
居：原意为蹲下。后来用踞字代替了本意。
等等。

B. 从履字来的，表示各种鞋子的字。履不是人体的部位，但是是服装，所以和尸的原意仍然有关联。(Derived from 履, used to represent various kinds of shoes. 履 is not the part of body, but the clothing, it's still relevant to the original meaning of 尸.)
这类字有：
屐：木鞋
屝：泛指鞋
屜：鞋子里垫的草。
屟（屧）：鞋子的木底
屣：鞋子
屦：麻鞋
等等

C.第三类的尸本意不是躯体，而是指房屋。其形状像一面墙壁和屋顶。(The meaning of the 3rd kind of 尸 is not body, but the house. Its shape looks like a wall and the roof.)
这类字有：
屋，
层（層）：原意指楼（重屋），引申为重，重复。
屏：原意指影壁墙。


2. About 户 (and 房)
户 means single leaf door originally, note it's not exactly the same but relevant to house.

象形。甲骨文字形,象门(門)字的一半。汉字部首之一。从“户”的多与门户有关。本义:单扇门

Here's a picture from the book &quot;字源谈趣&quot; explaining the difference between 门 and 户, especially their ancient form (left-most one).

Now we could understand the original meaning of 房, i.e. 正室左右的住室 (wing room/side room (with single door))

上古边室皆用单扇门(即“户”),庙门大门才用双扇门,故“房”从“户”。本义:正室左右的住室

Additional information about 居
居 seems to be the different case with 屋.

象形。金文字形,是“踞”的本字,象人曲胫蹲踞形。本义:蹲着

居 is the original character of 踞, means squat. Then it was used for other meanings, 踞 was created for the using of the meaning squat. So the usage of 尸 in 居 should be the 1st case shown as before.