Also, must all cancer cells have mutant or suppressed p53? Or are there any cancer cells that remain malignant despite having wild type p53 that is not surpressed?
It's been a while since I've worked on p53 but if I recall then cancer cells can upregulate the negative regulator MDM2 (which binds p53, thereby rendering it inactive). Thus, you have wild type p53 but still no activity. Have a look, I think Wikipedia actually explains parts of that. And second, even though p53 is mutated in very many cancer lines, there are many more proteins that can render a cell malignant without p53 being affected. Examples would be myc, RAS, different growth factors, other apoptosis regulators apart from p53, and literally dozens of other proteins, so-called oncogenes or proto-oncogenes. Also, normally more than one gene is affected before a cell turns malignant.
Loss of p53 function contributes to tumor progression through a combination of increased genetic instability, loss of growth-arresting signals, addition to oncogene .
The simple answer is P53 is not a direct supressor of its target genes. It is an activator of P21 WAF1/CIP (main mechanism, by stabilising the transcription promotion suppressiong DREAM complex), mdm2 and bbc3. If these genes, expecially p21 are mutated or suppressed in any other way, p53 wt does have at least less or no effect.