I think written and spoken language differs considerably. In Biber's (1988) MDA, demonstrative pronouns such as this, that, these, those are a feature positively weighted on Dimension 1, which is a very important indicator of "oralness".
Therefore, zhe and na occur in the LDC Callhome Mandain Corpus (about 30 million words of telephone conversation between Chinese nationals overseas and their families in China) over 3.2 times as frequently as in LCMC.
In Callhome, the ratio of zhe/na is 0.62, but in LCMC it is 2.65. This is probably because of the nature of telephone conversation.
Frequencies in Callhome:
这:2124
这个:1358
这么:200
这么着:1
这些:107
这会儿:1
这儿:148
这样:432
这边:331
这里:117
那:3418
那个:2957
那么:415
那些:90
那会儿:2
那儿:181
那天:68
那时:10
那样:91
那种:141
那边:261
那里:81