Quite a reduction of visible forms.

Google N-gram Corpus Counts
╭─ーーー─┬─────────┬───────╮
│ 住処　 │ 164.448 │ 28.8% │ /
│ 栖　　 │ 161.770 │  N/A  │Duplicates
│ 棲家　 │ 103.719 │ 18.1% │Sankoku, Nikk, Daijs, Jitsuyou; Was previously mentioned to be a frequent name; not moving higher
│ 住みか │  39.508 │  6.9% │Shinsen and GendaiSK
│ 住家　 │  37.086 │  6.5% │Saito, Shinsen, Daijs
│ 住み家 │  16.099 │  2.8% │Sankoku, Meikyo, GendaiSK, GendaiRK, Daijs; okurigana variant; [sK]
│ 棲み家 │  13.043 │  2.3% │Daijs; okurigana variant; [sK]
│ 住み処 │   8.703 │  1.5% │Sankoku, Meikyo, etc. ; okurigana variant; [sK]
│ 棲み処 │   6.390 │  1.1% │Sankoku, Iwakoku; Sankoku has this in a separate entry as "動物のすむ所。" ; [rK]
│ 棲処　 │   2.708 │  0.5% │Nikk
│ すみか │ 179.983 │ 31.5% │ /
╰─ーーー─┴─────────┴───────╯
╭─ーー─┬─────┬───────╮
│ 栖家 │ 330 │100.0% │scannable with daijs; 栖 is（繁体字, 正字） of 棲; add; [sK]
╰─ーー─┴─────┴───────╯
Nikkoku, Meikyo, Koj, Smk, Iwakoku: （「か」は、場所、ところの意。「家」はあて字）

三省堂 現代新国語辞典 第七版
すみか【住みか・住み家・住（み）処】〖栖〗
   ❶ 住んで生活している所。
      ［古風な言い方］類語：住まい・住居
   ❷ 〖棲み処〗動物のすむ所。

［比較］
  〚住みか〛人間にも動物にも使う。よくない者たちの住みついている所をさすことも多い。
      「盗賊のー」
  〚住まい〛人が住む所として、普通に使う。
      「快適なー」




Furigana.info:
語句	割合
ーーーーーーー
住家	32.8% see above
棲家	29.3% see above 
棲処	7.6% see above 
住処	7.1% see above
栖家	4.5% see above
栖	4.5% see above
棲所	3.5% /
住所	2.0% / 
棲	2.0% Smk Note; add; [sK]
栖所	1.0% /
住宅	1.0% /
栖処	1.0% /
棲居	0.5% /
棲巣	0.5% /
住居地	0.5% /
住換	0.5% /
住處	0.5% /
巣窟	0.5% /
棲處	0.5% /

Is [ateji] applied if only part of the kanji are ateji?

Reduced the surface forms a bit
Maybe we should have another sense for an animal's nest, habitat, etc. with the note "esp. 棲み処". Both Sankoku and GendaiSK indicate that that kanji form is specific for that sense, but most others don't

@@ -11,3 +10,0 @@
-<keb>住み家</keb>
-</k_ele>
-<k_ele>
@@ -15,3 +11,0 @@
-</k_ele>
-<k_ele>
-<keb>住み処</keb>
@@ -23,3 +16,0 @@
-<keb>棲み家</keb>
-</k_ele>
-<k_ele>
@@ -26,0 +18 @@
+<ke_inf>&rK;</ke_inf>
@@ -32,0 +25,12 @@
+<keb>住み家</keb>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
+<k_ele>
+<keb>棲み家</keb>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
+<k_ele>
+<keb>住み処</keb>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
+<k_ele>
@@ -33,0 +38,8 @@
+<ke_inf>&sK;</ke_inf>
+</k_ele>
+<k_ele>
+<keb>棲</keb>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
+<k_ele>
+<keb>栖家</keb>

A lot of visible forms.

daijr: 住む所。住まい。住居。現代では好ましくないものの住んでいる所をいうことが多い。「犯人の―を捜す」「鬼の―」
棲み家	13,043
棲処	2,708

The word itself often has negative connotations, regardless of what kanji are used. Daijs and smk have two senses.
棲家 doesn't have negative connotations (or refer to animals) in 終の棲家.
I think the 栖 count is mostly false positives.
住家 is usually じゅうか. Only daijs and nikk have 住家 for すみか. I think じゅうか should be a separate entry.

@@ -11 +11 @@
-<keb>住家</keb>
+<keb>住み家</keb>
@@ -14 +14 @@
-<keb>住み家</keb>
+<keb>住家</keb>
@@ -20,2 +20 @@
-<keb>棲み処</keb>
-<ke_inf>&rK;</ke_inf>
+<keb>棲家</keb>
@@ -24,2 +23,4 @@
-<keb>棲家</keb>
-<ke_inf>&rK;</ke_inf>
+<keb>棲み家</keb>
+</k_ele>
+<k_ele>
+<keb>棲み処</keb>
@@ -30,0 +32,4 @@
+<k_ele>
+<keb>棲処</keb>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
@@ -34,4 +38,0 @@
-<r_ele>
-<reb>じゅうか</reb>
-<re_restr>住家</re_restr>
-</r_ele>
@@ -40 +40,0 @@
-<xref type="see" seq="1595750">住い・1</xref>
@@ -42,0 +43 @@
+<gloss>home</gloss>
@@ -44 +45 @@
-<gloss>den</gloss>
+<gloss>abode</gloss>
@@ -45,0 +47,5 @@
+</sense>
+<sense>
+<pos>&n;</pos>
+<gloss>den (of criminals, demons, etc.)</gloss>
+<gloss>nest</gloss>

sankoku, daijr/s

Google N-gram Corpus Counts
╭─ーーー─┬─────────┬───────╮
│ 住処　 │ 164,448 │ 30.6% │
│ 住みか │  39,508 │  7.3% │
│ 住家　 │  37,086 │  6.9% │
│ 住み家 │  16,099 │  3.0% │
│ 住み処 │   8,703 │  1.6% │
│ 棲み処 │   6,390 │  1.2% │
│ 棲家　 │ 103,719 │ 19.3% │
│ 栖　　 │ 161,770 │ 30.1% │
╰─ーーー─┴─────────┴───────╯

棲み処, 棲家 and 栖 have negative connotations (+ inhabiting of animals) so i think they should be separated

@@ -20,0 +21 @@
+<ke_inf>&rK;</ke_inf>
@@ -23,0 +25 @@
+<ke_inf>&rK;</ke_inf>
@@ -26,0 +29 @@
+<ke_inf>&rK;</ke_inf>